From 76fc0ebaf1476c24a430d1f174b0e9b86d3c1f49 Mon Sep 17 00:00:00 2001
From: wolf <wolf@0785d39b-7218-0410-832d-ea1e28bc413d>
Date: Fri, 2 Sep 2005 15:23:01 +0000
Subject: [PATCH] Regenerate formulas.

git-svn-id: https://svn.dealii.org/trunk@11359 0785d39b-7218-0410-832d-ea1e28bc413d
---
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 101 files changed, 366 insertions(+), 266 deletions(-)

diff --git a/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro.html b/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro.html
index 57ad2e5ffe..5b8eeb9c1a 100644
--- a/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro.html
+++ b/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro.html
@@ -46,13 +46,14 @@ elastic wave equation
 <DIV ALIGN="CENTER"><TABLE CELLPADDING="0" WIDTH="100%" ALIGN="CENTER">
 <TR VALIGN="MIDDLE">
 <TD NOWRAP ALIGN="CENTER"><IMG
- WIDTH="221" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
+ WIDTH="223" HEIGHT="57" ALIGN="MIDDLE" BORDER="0"
  SRC="step-18.data/intro/img1.png"
  ALT="$\displaystyle \rho \frac{\partial^2 \vec u}{\partial t^2} + c \frac{\partial \vec u}{\partial t} - \div ( C \varepsilon(\vec u)) = \vec f$">&nbsp; &nbsp;in <IMG
- WIDTH="15" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
+ WIDTH="16" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
  SRC="step-18.data/intro/img2.png"
- ALT="$ \Omega$"><IMG
- WIDTH="7" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
+ ALT="$ \Omega$">
+<IMG
+ WIDTH="9" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
  SRC="step-18.data/intro/img3.png"
  ALT="$\displaystyle ,$"></TD>
 <TD NOWRAP WIDTH="10" ALIGN="RIGHT">
@@ -63,31 +64,36 @@ where <!-- MATH
  $\vec u=\vec u (\vec x,t)$
  -->
 <IMG
- WIDTH="79" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
+ WIDTH="81" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
  SRC="step-18.data/intro/img4.png"
- ALT="$ \vec u=\vec u (\vec x,t)$"> is the deformation of the body, <IMG
- WIDTH="11" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
+ ALT="$ \vec u=\vec u (\vec x,t)$">
+ is the deformation of the body, <IMG
+ WIDTH="13" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
  SRC="step-18.data/intro/img5.png"
  ALT="$ \rho$">
+
 and <IMG
- WIDTH="10" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
+ WIDTH="11" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
  SRC="step-18.data/intro/img6.png"
- ALT="$ c$"> the density and attenuation coefficient, and <IMG
- WIDTH="10" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
+ ALT="$ c$">
+ the density and attenuation coefficient, and <IMG
+ WIDTH="12" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
  SRC="step-18.data/intro/img7.png"
- ALT="$ \vec f$"> external forces.
+ ALT="$ \vec f$">
+ external forces.
 In addition, initial conditions
 <P></P>
 <DIV ALIGN="CENTER"><TABLE CELLPADDING="0" WIDTH="100%" ALIGN="CENTER">
 <TR VALIGN="MIDDLE">
 <TD NOWRAP ALIGN="CENTER"><IMG
- WIDTH="100" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
+ WIDTH="102" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
  SRC="step-18.data/intro/img8.png"
  ALT="$\displaystyle \vec u(\cdot, 0) = \vec u_0(\cdot)$">&nbsp; &nbsp;on <IMG
- WIDTH="15" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
+ WIDTH="16" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
  SRC="step-18.data/intro/img2.png"
- ALT="$ \Omega$"><IMG
- WIDTH="7" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
+ ALT="$ \Omega$">
+<IMG
+ WIDTH="9" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
  SRC="step-18.data/intro/img3.png"
  ALT="$\displaystyle ,$"></TD>
 <TD NOWRAP WIDTH="10" ALIGN="RIGHT">
@@ -100,11 +106,11 @@ to be specified for a unique solution:
 <DIV ALIGN="CENTER"><TABLE CELLPADDING="0" WIDTH="100%" ALIGN="CENTER">
 <TR VALIGN="MIDDLE">
 <TD NOWRAP ALIGN="RIGHT"><IMG
- WIDTH="48" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
+ WIDTH="49" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
  SRC="step-18.data/intro/img9.png"
  ALT="$\displaystyle \vec u(\vec x,t)$"></TD>
 <TD NOWRAP ALIGN="LEFT"><IMG
- WIDTH="97" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
+ WIDTH="98" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
  SRC="step-18.data/intro/img10.png"
  ALT="$\displaystyle = \vec d(\vec x,t) \qquad$"></TD>
 <TD>&nbsp;</TD>
@@ -112,21 +118,22 @@ to be specified for a unique solution:
  $\Gamma_D\subset\partial\Omega$
  -->
 <IMG
- WIDTH="67" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
+ WIDTH="68" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
  SRC="step-18.data/intro/img11.png"
- ALT="$ \Gamma_D\subset\partial\Omega$"><IMG
- WIDTH="7" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
+ ALT="$ \Gamma_D\subset\partial\Omega$">
+<IMG
+ WIDTH="9" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
  SRC="step-18.data/intro/img3.png"
  ALT="$\displaystyle ,$"></TD>
 <TD NOWRAP WIDTH="10" ALIGN="RIGHT">
 (3)</TD></TR>
 <TR VALIGN="MIDDLE">
 <TD NOWRAP ALIGN="RIGHT"><IMG
- WIDTH="96" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
+ WIDTH="97" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
  SRC="step-18.data/intro/img12.png"
- ALT="$\displaystyle \vec n  C \varepsilon(\vec u(\vec x,t))$"></TD>
+ ALT="$\displaystyle \vec n \ C \varepsilon(\vec u(\vec x,t))$"></TD>
 <TD NOWRAP ALIGN="LEFT"><IMG
- WIDTH="97" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
+ WIDTH="98" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
  SRC="step-18.data/intro/img13.png"
  ALT="$\displaystyle = \vec b(\vec x,t) \qquad$"></TD>
 <TD>&nbsp;</TD>
@@ -134,10 +141,11 @@ to be specified for a unique solution:
  $\Gamma_N=\partial\Omega\backslash\Gamma_D$
  -->
 <IMG
- WIDTH="97" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
+ WIDTH="98" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
  SRC="step-18.data/intro/img14.png"
- ALT="$ \Gamma_N=\partial\Omega\backslash\Gamma_D$"><IMG
- WIDTH="7" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
+ ALT="$ \Gamma_N=\partial\Omega\backslash\Gamma_D$">
+<IMG
+ WIDTH="9" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
  SRC="step-18.data/intro/img15.png"
  ALT="$\displaystyle .$"></TD>
 <TD NOWRAP WIDTH="10" ALIGN="RIGHT">
@@ -149,43 +157,50 @@ In above formulation, <!-- MATH
 \vec u^T)$
  -->
 <IMG
- WIDTH="153" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
+ WIDTH="155" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
  SRC="step-18.data/intro/img16.png"
  ALT="$ \varepsilon(\vec u)= \tfrac 12 (\nabla \vec u + \nabla
-\vec u^T)$"> is the symmetric gradient of the displacement, also called the
+\vec u^T)$">
+ is the symmetric gradient of the displacement, also called the
 <I>strain</I>. <IMG
- WIDTH="16" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
+ WIDTH="17" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
  SRC="step-18.data/intro/img17.png"
- ALT="$ C$"> is a tensor of rank 4, called the <I>stress-strain
+ ALT="$ C$">
+ is a tensor of rank 4, called the <I>stress-strain
   tensor</I> that contains knowledge of the elastic strength of the material; its
 symmetry properties make sure that it maps symmetric tensors of rank 2
 (``matrices'' of dimension <IMG
- WIDTH="11" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
+ WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
  SRC="step-18.data/intro/img18.png"
- ALT="$ d$">, where <IMG
- WIDTH="11" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
+ ALT="$ d$">
+, where <IMG
+ WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
  SRC="step-18.data/intro/img18.png"
- ALT="$ d$"> is the spatial dimensionality) onto
+ ALT="$ d$">
+ is the spatial dimensionality) onto
 symmetric tensors of the same rank. We will comment on the roles of the strain
 and stress tensors more below. For the moment it suffices to say that we
 interpret the term <!-- MATH
  $\div ( C \varepsilon(\vec u))$
  -->
 <IMG
- WIDTH="85" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
+ WIDTH="87" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
  SRC="step-18.data/intro/img19.png"
- ALT="$ \div ( C \varepsilon(\vec u))$"> as the vector with
+ ALT="$ \div ( C \varepsilon(\vec u))$">
+ as the vector with
 components <!-- MATH
  $\tfrac \partial{\partial x_j} C_{ijkl} \varepsilon(\vec u)_{kl}$
  -->
 <IMG
- WIDTH="103" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
+ WIDTH="105" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
  SRC="step-18.data/intro/img20.png"
- ALT="$ \tfrac \partial{\partial x_j} C_{ijkl} \varepsilon(\vec u)_{kl}$">,
+ ALT="$ \tfrac \partial{\partial x_j} C_{ijkl} \varepsilon(\vec u)_{kl}$">
+,
 where summation over indices <IMG
- WIDTH="38" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
+ WIDTH="39" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
  SRC="step-18.data/intro/img21.png"
- ALT="$ j,k,l$"> is implied.
+ ALT="$ j,k,l$">
+ is implied.
 
 <P>
 The quasistatic limit of this equation is motivated as follows: each small
@@ -194,71 +209,76 @@ forcing function, will result in a corresponding change in the configuration
 of the body. In general, this will be in the form of waves radiating away from
 the location of the disturbance. Due to the presence of the damping term,
 these waves will be attenuated on a time scale of, say, <IMG
- WIDTH="12" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
+ WIDTH="13" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
  SRC="step-18.data/intro/img22.png"
- ALT="$ \tau$">. Now, assume
+ ALT="$ \tau$">
+. Now, assume
 that all changes in external forcing happen on times scales that are
 much larger than <IMG
- WIDTH="12" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
+ WIDTH="13" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
  SRC="step-18.data/intro/img22.png"
- ALT="$ \tau$">. In that case, the dynamic nature of the change is
+ ALT="$ \tau$">
+. In that case, the dynamic nature of the change is
 unimportant: we can consider the body to always be in static equilibrium,
 i.e.&nbsp;we can assume that at all times the body satisfies
 <P></P>
 <DIV ALIGN="CENTER"><TABLE CELLPADDING="0" WIDTH="100%" ALIGN="CENTER">
 <TR VALIGN="MIDDLE">
 <TD NOWRAP ALIGN="RIGHT"><IMG
- WIDTH="97" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
+ WIDTH="99" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
  SRC="step-18.data/intro/img23.png"
  ALT="$\displaystyle - \div ( C \varepsilon(\vec u))$"></TD>
 <TD NOWRAP ALIGN="LEFT"><IMG
- WIDTH="27" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
+ WIDTH="29" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
  SRC="step-18.data/intro/img24.png"
  ALT="$\displaystyle = \vec f$"></TD>
 <TD>&nbsp;</TD>
 <TD NOWRAP ALIGN="LEFT">in <IMG
- WIDTH="15" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
+ WIDTH="16" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
  SRC="step-18.data/intro/img2.png"
- ALT="$ \Omega$"><IMG
- WIDTH="7" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
+ ALT="$ \Omega$">
+<IMG
+ WIDTH="9" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
  SRC="step-18.data/intro/img3.png"
  ALT="$\displaystyle ,$"></TD>
 <TD NOWRAP WIDTH="10" ALIGN="RIGHT">
 (5)</TD></TR>
 <TR VALIGN="MIDDLE">
 <TD NOWRAP ALIGN="RIGHT"><IMG
- WIDTH="48" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
+ WIDTH="49" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
  SRC="step-18.data/intro/img9.png"
  ALT="$\displaystyle \vec u(\vec x,t)$"></TD>
 <TD NOWRAP ALIGN="LEFT"><IMG
- WIDTH="97" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
+ WIDTH="98" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
  SRC="step-18.data/intro/img10.png"
  ALT="$\displaystyle = \vec d(\vec x,t) \qquad$"></TD>
 <TD>&nbsp;</TD>
 <TD NOWRAP ALIGN="LEFT">on <IMG
- WIDTH="25" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
+ WIDTH="26" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
  SRC="step-18.data/intro/img25.png"
- ALT="$ \Gamma_D$"><IMG
- WIDTH="7" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
+ ALT="$ \Gamma_D$">
+<IMG
+ WIDTH="9" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
  SRC="step-18.data/intro/img3.png"
  ALT="$\displaystyle ,$"></TD>
 <TD NOWRAP WIDTH="10" ALIGN="RIGHT">
 (6)</TD></TR>
 <TR VALIGN="MIDDLE">
 <TD NOWRAP ALIGN="RIGHT"><IMG
- WIDTH="96" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
+ WIDTH="97" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
  SRC="step-18.data/intro/img12.png"
- ALT="$\displaystyle \vec n  C \varepsilon(\vec u(\vec x,t))$"></TD>
+ ALT="$\displaystyle \vec n \ C \varepsilon(\vec u(\vec x,t))$"></TD>
 <TD NOWRAP ALIGN="LEFT"><IMG
- WIDTH="97" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
+ WIDTH="98" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
  SRC="step-18.data/intro/img13.png"
  ALT="$\displaystyle = \vec b(\vec x,t) \qquad$"></TD>
 <TD>&nbsp;</TD>
 <TD NOWRAP ALIGN="LEFT">on <IMG
- WIDTH="25" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
+ WIDTH="26" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
  SRC="step-18.data/intro/img26.png"
- ALT="$ \Gamma_N$"><IMG
- WIDTH="7" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
+ ALT="$ \Gamma_N$">
+<IMG
+ WIDTH="9" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
  SRC="step-18.data/intro/img15.png"
  ALT="$\displaystyle .$"></TD>
 <TD NOWRAP WIDTH="10" ALIGN="RIGHT">
@@ -271,46 +291,49 @@ possibly time-varying force function <!-- MATH
  $\vec f(\vec x,t)$
  -->
 <IMG
- WIDTH="45" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
+ WIDTH="47" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
  SRC="step-18.data/intro/img27.png"
- ALT="$ \vec f(\vec x,t)$">.
+ ALT="$ \vec f(\vec x,t)$">
+.
 
 <P>
 While these equations are sufficient to describe small deformations, computing
 large deformations is a little more complicated. To do so, let us first
 introduce a stress variable <IMG
- WIDTH="13" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
+ WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
  SRC="step-18.data/intro/img28.png"
- ALT="$ \sigma$">, and write the differential equations in
+ ALT="$ \sigma$">
+, and write the differential equations in
 terms of the stress:
 <P></P>
 <DIV ALIGN="CENTER"><TABLE CELLPADDING="0" WIDTH="100%" ALIGN="CENTER">
 <TR VALIGN="MIDDLE">
 <TD NOWRAP ALIGN="RIGHT"><IMG
- WIDTH="52" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
+ WIDTH="54" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
  SRC="step-18.data/intro/img29.png"
  ALT="$\displaystyle - \div\sigma$"></TD>
 <TD NOWRAP ALIGN="LEFT"><IMG
- WIDTH="27" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
+ WIDTH="29" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
  SRC="step-18.data/intro/img24.png"
  ALT="$\displaystyle = \vec f$"></TD>
 <TD>&nbsp;</TD>
 <TD NOWRAP ALIGN="LEFT">in <IMG
- WIDTH="33" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
+ WIDTH="34" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
  SRC="step-18.data/intro/img30.png"
- ALT="$ \Omega(t)$"><IMG
- WIDTH="7" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
+ ALT="$ \Omega(t)$">
+<IMG
+ WIDTH="9" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
  SRC="step-18.data/intro/img3.png"
  ALT="$\displaystyle ,$"></TD>
 <TD NOWRAP WIDTH="10" ALIGN="RIGHT">
 (8)</TD></TR>
 <TR VALIGN="MIDDLE">
 <TD NOWRAP ALIGN="RIGHT"><IMG
- WIDTH="48" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
+ WIDTH="49" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
  SRC="step-18.data/intro/img9.png"
  ALT="$\displaystyle \vec u(\vec x,t)$"></TD>
 <TD NOWRAP ALIGN="LEFT"><IMG
- WIDTH="97" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
+ WIDTH="98" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
  SRC="step-18.data/intro/img10.png"
  ALT="$\displaystyle = \vec d(\vec x,t) \qquad$"></TD>
 <TD>&nbsp;</TD>
@@ -318,21 +341,22 @@ terms of the stress:
  $\Gamma_D\subset\partial\Omega(t)$
  -->
 <IMG
- WIDTH="85" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
+ WIDTH="86" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
  SRC="step-18.data/intro/img31.png"
- ALT="$ \Gamma_D\subset\partial\Omega(t)$"><IMG
- WIDTH="7" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
+ ALT="$ \Gamma_D\subset\partial\Omega(t)$">
+<IMG
+ WIDTH="9" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
  SRC="step-18.data/intro/img3.png"
  ALT="$\displaystyle ,$"></TD>
 <TD NOWRAP WIDTH="10" ALIGN="RIGHT">
 (9)</TD></TR>
 <TR VALIGN="MIDDLE">
 <TD NOWRAP ALIGN="RIGHT"><IMG
- WIDTH="96" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
+ WIDTH="97" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
  SRC="step-18.data/intro/img12.png"
- ALT="$\displaystyle \vec n  C \varepsilon(\vec u(\vec x,t))$"></TD>
+ ALT="$\displaystyle \vec n \ C \varepsilon(\vec u(\vec x,t))$"></TD>
 <TD NOWRAP ALIGN="LEFT"><IMG
- WIDTH="97" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
+ WIDTH="98" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
  SRC="step-18.data/intro/img13.png"
  ALT="$\displaystyle = \vec b(\vec x,t) \qquad$"></TD>
 <TD>&nbsp;</TD>
@@ -340,10 +364,11 @@ terms of the stress:
  $\Gamma_N=\partial\Omega(t)\backslash\Gamma_D$
  -->
 <IMG
- WIDTH="115" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
+ WIDTH="116" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
  SRC="step-18.data/intro/img32.png"
- ALT="$ \Gamma_N=\partial\Omega(t)\backslash\Gamma_D$"><IMG
- WIDTH="7" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
+ ALT="$ \Gamma_N=\partial\Omega(t)\backslash\Gamma_D$">
+<IMG
+ WIDTH="9" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
  SRC="step-18.data/intro/img15.png"
  ALT="$\displaystyle .$"></TD>
 <TD NOWRAP WIDTH="10" ALIGN="RIGHT">
@@ -351,24 +376,26 @@ terms of the stress:
 </TABLE></DIV>
 <BR CLEAR="ALL"><P></P>
 Note that these equations are posed on a domain <IMG
- WIDTH="33" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
+ WIDTH="34" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
  SRC="step-18.data/intro/img30.png"
- ALT="$ \Omega(t)$"> that
+ ALT="$ \Omega(t)$">
+ that
 changes with time, with the boundary moving according to the
 displacements <!-- MATH
  $\vec u(\vec x,t)$
  -->
 <IMG
- WIDTH="48" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
+ WIDTH="49" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
  SRC="step-18.data/intro/img33.png"
- ALT="$ \vec u(\vec x,t)$"> of the points on the boundary. To
+ ALT="$ \vec u(\vec x,t)$">
+ of the points on the boundary. To
 complete this system, we have to specify the relationship between the
 stress and the strain, as follows:
 <P></P>
 <DIV ALIGN="CENTER"><TABLE CELLPADDING="0" WIDTH="100%" ALIGN="CENTER">
 <TR VALIGN="MIDDLE">
 <TD NOWRAP ALIGN="CENTER"><IMG
- WIDTH="81" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
+ WIDTH="82" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
  SRC="step-18.data/intro/img34.png"
  ALT="$\displaystyle \dot\sigma = C \varepsilon (\dot{\vec u}),$"></TD>
 <TD NOWRAP WIDTH="10" ALIGN="RIGHT">
@@ -376,16 +403,18 @@ stress and the strain, as follows:
 </TABLE></DIV>
 <BR CLEAR="ALL"><P></P>
 where a dot indicates a time derivative. Both the stress <IMG
- WIDTH="13" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
+ WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
  SRC="step-18.data/intro/img28.png"
- ALT="$ \sigma$"> and the
+ ALT="$ \sigma$">
+ and the
 strain <!-- MATH
  $\varepsilon(\vec u)$
  -->
 <IMG
- WIDTH="33" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
+ WIDTH="34" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
  SRC="step-18.data/intro/img35.png"
- ALT="$ \varepsilon(\vec u)$"> are symmetric tensors of rank 2.
+ ALT="$ \varepsilon(\vec u)$">
+ are symmetric tensors of rank 2.
 
 <P>
 
@@ -397,14 +426,15 @@ Time discretization</A>
 Numerically, this system is solved as follows: first, we discretize
 the time component using a backward Euler scheme. This leads to a
 discrete equilibrium of force at time step <IMG
- WIDTH="13" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
+ WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
  SRC="step-18.data/intro/img36.png"
- ALT="$ n$">:
+ ALT="$ n$">
+:
 <P></P>
 <DIV ALIGN="CENTER"><TABLE CELLPADDING="0" WIDTH="100%" ALIGN="CENTER">
 <TR VALIGN="MIDDLE">
 <TD NOWRAP ALIGN="CENTER"><IMG
- WIDTH="105" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
+ WIDTH="106" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
  SRC="step-18.data/intro/img37.png"
  ALT="$\displaystyle -\div\sigma^n = f^n,$"></TD>
 <TD NOWRAP WIDTH="10" ALIGN="RIGHT">
@@ -416,7 +446,7 @@ where
 <DIV ALIGN="CENTER"><TABLE CELLPADDING="0" WIDTH="100%" ALIGN="CENTER">
 <TR VALIGN="MIDDLE">
 <TD NOWRAP ALIGN="CENTER"><IMG
- WIDTH="165" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
+ WIDTH="167" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
  SRC="step-18.data/intro/img38.png"
  ALT="$\displaystyle \sigma^n = \sigma^{n-1} + C \varepsilon (\Delta \vec u^n),$"></TD>
 <TD NOWRAP WIDTH="10" ALIGN="RIGHT">
@@ -427,23 +457,25 @@ and <!-- MATH
  $\Delta \vec u^n$
  -->
 <IMG
- WIDTH="35" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
+ WIDTH="37" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
  SRC="step-18.data/intro/img39.png"
- ALT="$ \Delta \vec u^n$"> the incremental displacement for time step
+ ALT="$ \Delta \vec u^n$">
+ the incremental displacement for time step
 <IMG
- WIDTH="13" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
+ WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
  SRC="step-18.data/intro/img36.png"
- ALT="$ n$">. This way, if we want to solve for the displacement increment, we
+ ALT="$ n$">
+. This way, if we want to solve for the displacement increment, we
 have to solve the following system:
 <P></P>
 <DIV ALIGN="CENTER"><TABLE CELLPADDING="0" WIDTH="100%" ALIGN="CENTER">
 <TR VALIGN="MIDDLE">
 <TD NOWRAP ALIGN="RIGHT"><IMG
- WIDTH="107" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
+ WIDTH="108" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
  SRC="step-18.data/intro/img40.png"
  ALT="$\displaystyle - \div C \varepsilon(\Delta\vec u^n)$"></TD>
 <TD NOWRAP ALIGN="LEFT"><IMG
- WIDTH="108" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
+ WIDTH="110" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
  SRC="step-18.data/intro/img41.png"
  ALT="$\displaystyle = \vec f + \div\sigma^{n-1}$"></TD>
 <TD>&nbsp;</TD>
@@ -451,21 +483,22 @@ have to solve the following system:
  $\Omega(t_{n-1})$
  -->
 <IMG
- WIDTH="58" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
+ WIDTH="59" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
  SRC="step-18.data/intro/img42.png"
- ALT="$ \Omega(t_{n-1})$"><IMG
- WIDTH="7" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
+ ALT="$ \Omega(t_{n-1})$">
+<IMG
+ WIDTH="9" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
  SRC="step-18.data/intro/img3.png"
  ALT="$\displaystyle ,$"></TD>
 <TD NOWRAP WIDTH="10" ALIGN="RIGHT">
 (14)</TD></TR>
 <TR VALIGN="MIDDLE">
 <TD NOWRAP ALIGN="RIGHT"><IMG
- WIDTH="70" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
+ WIDTH="71" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
  SRC="step-18.data/intro/img43.png"
  ALT="$\displaystyle \Delta \vec u^n(\vec x,t)$"></TD>
 <TD NOWRAP ALIGN="LEFT"><IMG
- WIDTH="195" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
+ WIDTH="196" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
  SRC="step-18.data/intro/img44.png"
  ALT="$\displaystyle = \vec d(\vec x,t_n) - \vec d(\vec x,t_{n-1}) \qquad$"></TD>
 <TD>&nbsp;</TD>
@@ -473,21 +506,22 @@ have to solve the following system:
  $\Gamma_D\subset\partial\Omega(t_{n-1})$
  -->
 <IMG
- WIDTH="110" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
+ WIDTH="111" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
  SRC="step-18.data/intro/img45.png"
- ALT="$ \Gamma_D\subset\partial\Omega(t_{n-1})$"><IMG
- WIDTH="7" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
+ ALT="$ \Gamma_D\subset\partial\Omega(t_{n-1})$">
+<IMG
+ WIDTH="9" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
  SRC="step-18.data/intro/img3.png"
  ALT="$\displaystyle ,$"></TD>
 <TD NOWRAP WIDTH="10" ALIGN="RIGHT">
 (15)</TD></TR>
 <TR VALIGN="MIDDLE">
 <TD NOWRAP ALIGN="RIGHT"><IMG
- WIDTH="118" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
+ WIDTH="119" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
  SRC="step-18.data/intro/img46.png"
- ALT="$\displaystyle \vec n  C \varepsilon(\Delta \vec u^n(\vec x,t))$"></TD>
+ ALT="$\displaystyle \vec n \ C \varepsilon(\Delta \vec u^n(\vec x,t))$"></TD>
 <TD NOWRAP ALIGN="LEFT"><IMG
- WIDTH="195" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
+ WIDTH="196" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
  SRC="step-18.data/intro/img47.png"
  ALT="$\displaystyle = \vec b(\vec x,t_n)-\vec b(\vec x,t_{n-1}) \qquad$"></TD>
 <TD>&nbsp;</TD>
@@ -495,10 +529,11 @@ have to solve the following system:
  $\Gamma_N=\partial\Omega(t_{n-1})\backslash\Gamma_D$
  -->
 <IMG
- WIDTH="140" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
+ WIDTH="141" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
  SRC="step-18.data/intro/img48.png"
- ALT="$ \Gamma_N=\partial\Omega(t_{n-1})\backslash\Gamma_D$"><IMG
- WIDTH="7" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
+ ALT="$ \Gamma_N=\partial\Omega(t_{n-1})\backslash\Gamma_D$">
+<IMG
+ WIDTH="9" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
  SRC="step-18.data/intro/img15.png"
  ALT="$\displaystyle .$"></TD>
 <TD NOWRAP WIDTH="10" ALIGN="RIGHT">
@@ -511,10 +546,11 @@ finite element formulation, reads as follows: find <!-- MATH
 \{v\in H^1(\Omega(t_{n-1}))^d: v|_{\Gamma_D}=\vec d(\cdot,t_n) - \vec d(\cdot,t_{n-1})\}$
  -->
 <IMG
- WIDTH="393" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
+ WIDTH="394" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
  SRC="step-18.data/intro/img49.png"
  ALT="$ \Delta \vec u^n \in
 \{v\in H^1(\Omega(t_{n-1}))^d: v\vert _{\Gamma_D}=\vec d(\cdot,t_n) - \vec d(\cdot,t_{n-1})\}$">
+
 such that
 <P></P>
 <DIV ALIGN="CENTER"><TABLE CELLPADDING="0" WIDTH="100%" ALIGN="CENTER">
@@ -533,58 +569,67 @@ are no boundary forces, i.e.&nbsp;<!-- MATH
  $\vec b = 0$
  -->
 <IMG
- WIDTH="42" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
+ WIDTH="44" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
  SRC="step-18.data/intro/img51.png"
- ALT="$ \vec b = 0$">, and that the deformation of the
+ ALT="$ \vec b = 0$">
+, and that the deformation of the
 body is driven by body forces <IMG
- WIDTH="10" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
+ WIDTH="12" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
  SRC="step-18.data/intro/img7.png"
- ALT="$ \vec f$"> and prescribed boundary displacements
+ ALT="$ \vec f$">
+ and prescribed boundary displacements
 <IMG
- WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
+ WIDTH="15" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
  SRC="step-18.data/intro/img52.png"
- ALT="$ \vec d$"> alone. It is also worth noting that when integrating by parts, we
+ ALT="$ \vec d$">
+ alone. It is also worth noting that when integrating by parts, we
 would get terms of the form <!-- MATH
  $(C \varepsilon(\Delta\vec u^n), \nabla \varphi
 )_{\Omega(t_{n-1})}$
  -->
 <IMG
- WIDTH="157" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
+ WIDTH="158" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
  SRC="step-18.data/intro/img53.png"
  ALT="$ (C \varepsilon(\Delta\vec u^n), \nabla \varphi
-)_{\Omega(t_{n-1})}$">, but that we replace it with the term involving the
+)_{\Omega(t_{n-1})}$">
+, but that we replace it with the term involving the
 symmetric gradient <!-- MATH
  $\varepsilon(\varphi)$
  -->
 <IMG
- WIDTH="33" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
+ WIDTH="35" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
  SRC="step-18.data/intro/img54.png"
- ALT="$ \varepsilon(\varphi)$"> instead of <!-- MATH
+ ALT="$ \varepsilon(\varphi)$">
+ instead of <!-- MATH
  $\nabla\varphi$
  -->
 <IMG
- WIDTH="27" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
+ WIDTH="28" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
  SRC="step-18.data/intro/img55.png"
- ALT="$ \nabla\varphi$">. Due to
+ ALT="$ \nabla\varphi$">
+. Due to
 the symmetry of <IMG
- WIDTH="16" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
+ WIDTH="17" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
  SRC="step-18.data/intro/img17.png"
- ALT="$ C$">, the two terms are equivalent, but the symmetric version
+ ALT="$ C$">
+, the two terms are equivalent, but the symmetric version
 avoids a potential for round-off to render the resulting matrix slightly
 non-symmetric.
 
 <P>
 The system at time step <IMG
- WIDTH="13" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
+ WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
  SRC="step-18.data/intro/img36.png"
- ALT="$ n$">, to be solved on the old domain
+ ALT="$ n$">
+, to be solved on the old domain
 <!-- MATH
  $\Omega(t_{n-1})$
  -->
 <IMG
- WIDTH="58" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
+ WIDTH="59" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
  SRC="step-18.data/intro/img42.png"
- ALT="$ \Omega(t_{n-1})$">, has exactly the form of a stationary elastic
+ ALT="$ \Omega(t_{n-1})$">
+, has exactly the form of a stationary elastic
 problem, and is therefore similar to what we have already implemented
 in previous example programs. We will therefore not comment on the
 space discretization beyond saying that we again use lowest order
@@ -603,9 +648,10 @@ There are differences, however:
  $\sigma^{n-1}$
  -->
 <IMG
- WIDTH="38" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
+ WIDTH="39" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
  SRC="step-18.data/intro/img56.png"
- ALT="$ \sigma^{n-1}$"> to compute the next incremental
+ ALT="$ \sigma^{n-1}$">
+ to compute the next incremental
   displacement, i.e.&nbsp;we need to compute it at the end of the time step
   to make sure it is available for the next time step. Essentially,
   the stress variable is our window to the history of deformation of
@@ -625,18 +671,20 @@ Updating the stress variable</A>
 
 <P>
 As indicated above, we need to have the stress variable <IMG
- WIDTH="21" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
+ WIDTH="23" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
  SRC="step-18.data/intro/img57.png"
- ALT="$ \sigma^n$"> available
+ ALT="$ \sigma^n$">
+ available
 when computing time step <IMG
- WIDTH="40" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
+ WIDTH="41" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
  SRC="step-18.data/intro/img58.png"
- ALT="$ n+1$">, and we can compute it using
+ ALT="$ n+1$">
+, and we can compute it using
 <P></P>
 <DIV ALIGN="CENTER"><TABLE CELLPADDING="0" WIDTH="100%" ALIGN="CENTER">
 <TR VALIGN="MIDDLE">
 <TD NOWRAP ALIGN="CENTER"><IMG
- WIDTH="165" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
+ WIDTH="167" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
  SRC="step-18.data/intro/img59.png"
  ALT="$\displaystyle \sigma^n = \sigma^{n-1} + C \varepsilon (\Delta \vec u^n).$"></TD>
 <TD NOWRAP WIDTH="10" ALIGN="RIGHT">
@@ -645,34 +693,39 @@ when computing time step <IMG
 <BR CLEAR="ALL"><P></P>
 There are, despite the apparent simplicity of this equation, two questions
 that we need to discuss. The first concerns the way we store <IMG
- WIDTH="21" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
+ WIDTH="23" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
  SRC="step-18.data/intro/img57.png"
- ALT="$ \sigma^n$">: even
+ ALT="$ \sigma^n$">
+: even
 if we compute the incremental updates <!-- MATH
  $\Delta\vec u^n$
  -->
 <IMG
- WIDTH="35" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
+ WIDTH="37" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
  SRC="step-18.data/intro/img39.png"
- ALT="$ \Delta \vec u^n$"> using lowest-order
+ ALT="$ \Delta \vec u^n$">
+ using lowest-order
 finite elements, then its symmetric gradient <!-- MATH
  $\varepsilon(\Delta\vec u^n)$
  -->
 <IMG
- WIDTH="55" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
+ WIDTH="56" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
  SRC="step-18.data/intro/img60.png"
- ALT="$ \varepsilon(\Delta\vec u^n)$"> is
+ ALT="$ \varepsilon(\Delta\vec u^n)$">
+ is
 in general still a function that is not easy to describe. In particular, it is
 not a piecewise constant function, and on general meshes (with cells that are
 not rectangles parallel to the coordinate axes) or with non-constant
 stress-strain tensors <IMG
- WIDTH="16" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
+ WIDTH="17" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
  SRC="step-18.data/intro/img17.png"
- ALT="$ C$"> it is not even a bi- or trilinear function. Thus, it
+ ALT="$ C$">
+ it is not even a bi- or trilinear function. Thus, it
 is a priori not clear how to store <IMG
- WIDTH="21" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
+ WIDTH="23" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
  SRC="step-18.data/intro/img57.png"
- ALT="$ \sigma^n$"> in a computer program.
+ ALT="$ \sigma^n$">
+ in a computer program.
 
 <P>
 To decide this, we have to see where it is used. The only place where we
@@ -681,40 +734,45 @@ require the stress is in the term
  $(\sigma^{n-1},\varepsilon(\varphi))_{\Omega(t_{n-1})}$
  -->
 <IMG
- WIDTH="134" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
+ WIDTH="135" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
  SRC="step-18.data/intro/img61.png"
- ALT="$ (\sigma^{n-1},\varepsilon(\varphi))_{\Omega(t_{n-1})}$">. In practice, we of
+ ALT="$ (\sigma^{n-1},\varepsilon(\varphi))_{\Omega(t_{n-1})}$">
+. In practice, we of
 course replace this term by numerical quadrature:
 <P></P>
 <DIV ALIGN="CENTER"><TABLE CELLPADDING="0" WIDTH="100%" ALIGN="CENTER">
 <TR VALIGN="MIDDLE">
 <TD NOWRAP ALIGN="CENTER"><IMG
- WIDTH="523" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
+ WIDTH="518" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
  SRC="step-18.data/intro/img62.png"
  ALT="$\displaystyle (\sigma^{n-1},\varepsilon(\varphi))_{\Omega(t_{n-1})} = \sum_{K\s...
-...thbb{T}}} \sum_q w_q  \sigma^{n-1}(\vec x_q) : \varepsilon(\varphi(\vec x_q)),$"></TD>
+...athbb{T}}} \sum_q w_q \ \sigma^{n-1}(\vec x_q) : \varepsilon(\varphi(\vec x_q),$"></TD>
 <TD NOWRAP WIDTH="10" ALIGN="RIGHT">
 (19)</TD></TR>
 </TABLE></DIV>
 <BR CLEAR="ALL"><P></P>
 where <IMG
- WIDTH="21" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
+ WIDTH="23" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
  SRC="step-18.data/intro/img63.png"
- ALT="$ w_q$"> are the quadrature weights and <IMG
- WIDTH="20" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
+ ALT="$ w_q$">
+ are the quadrature weights and <IMG
+ WIDTH="21" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
  SRC="step-18.data/intro/img64.png"
- ALT="$ \vec x_q$"> the quadrature points on
+ ALT="$ \vec x_q$">
+ the quadrature points on
 cell <IMG
- WIDTH="18" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
+ WIDTH="19" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
  SRC="step-18.data/intro/img65.png"
- ALT="$ K$">. This should make clear that what we really need is not the stress
+ ALT="$ K$">
+. This should make clear that what we really need is not the stress
 <!-- MATH
  $\sigma^{n-1}$
  -->
 <IMG
- WIDTH="38" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
+ WIDTH="39" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
  SRC="step-18.data/intro/img56.png"
- ALT="$ \sigma^{n-1}$"> in itself, but only the values of the stress in the quadrature
+ ALT="$ \sigma^{n-1}$">
+ in itself, but only the values of the stress in the quadrature
 points on all cells. This, however, is a simpler task: we only have to provide
 a data structure that is able to hold one symmetric tensor of rank 2 for each
 quadrature point on all cells (or, since we compute in parallel, all
@@ -723,22 +781,26 @@ end of each time step we then only have to evaluate <!-- MATH
  $\varepsilon(\Delta \vec u^n(\vec x_q))$
  -->
 <IMG
- WIDTH="84" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
+ WIDTH="85" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
  SRC="step-18.data/intro/img66.png"
- ALT="$ \varepsilon(\Delta \vec u^n(\vec x_q))$">, multiply it by the stress-strain tensor <IMG
- WIDTH="16" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
+ ALT="$ \varepsilon(\Delta \vec u^n(\vec x_q))$">
+, multiply it by the stress-strain tensor <IMG
+ WIDTH="17" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
  SRC="step-18.data/intro/img17.png"
- ALT="$ C$">, and use the
+ ALT="$ C$">
+, and use the
 result to update the stress <!-- MATH
  $\sigma^n(\vec x_q)$
  -->
 <IMG
- WIDTH="50" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
+ WIDTH="52" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
  SRC="step-18.data/intro/img67.png"
- ALT="$ \sigma^n(\vec x_q)$"> at quadrature point <IMG
- WIDTH="11" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
+ ALT="$ \sigma^n(\vec x_q)$">
+ at quadrature point <IMG
+ WIDTH="12" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
  SRC="step-18.data/intro/img68.png"
- ALT="$ q$">.
+ ALT="$ q$">
+.
 
 <P>
 The second complication is not visible in our notation as chosen above. It is
@@ -746,23 +808,26 @@ due to the fact that we compute <!-- MATH
  $\Delta u^n$
  -->
 <IMG
- WIDTH="34" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
+ WIDTH="36" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
  SRC="step-18.data/intro/img69.png"
- ALT="$ \Delta u^n$"> on the domain <!-- MATH
+ ALT="$ \Delta u^n$">
+ on the domain <!-- MATH
  $\Omega(t_{n-1})$
  -->
 <IMG
- WIDTH="58" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
+ WIDTH="59" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
  SRC="step-18.data/intro/img42.png"
- ALT="$ \Omega(t_{n-1})$">,
+ ALT="$ \Omega(t_{n-1})$">
+,
 and then use this displacement increment to both update the stress as well as
 move the mesh nodes around to get to <!-- MATH
  $\Omega(t_n)$
  -->
 <IMG
- WIDTH="41" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
+ WIDTH="43" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
  SRC="step-18.data/intro/img70.png"
- ALT="$ \Omega(t_n)$"> on which the next increment
+ ALT="$ \Omega(t_n)$">
+ on which the next increment
 is computed. What we have to make sure, in this context, is that moving the
 mesh does not only involve moving around the nodes, but also making
 corresponding changes to the stress variable: the updated stress is a variable
@@ -772,9 +837,10 @@ can be understood as follows: locally, the incremental deformation <!-- MATH
  $\Delta\vec u$
  -->
 <IMG
- WIDTH="26" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
+ WIDTH="28" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
  SRC="step-18.data/intro/img71.png"
- ALT="$ \Delta\vec u$"> can be decomposed into three parts, a linear translation (the constant part
+ ALT="$ \Delta\vec u$">
+ can be decomposed into three parts, a linear translation (the constant part
 of the displacement field in the neighborhood of a point), a dilational
 component (that part of the gradient of the displacement field that has a
 nonzero divergence), and a rotation. A linear translation of the material does
@@ -786,48 +852,54 @@ situation where <!-- MATH
  $\Delta\vec u=(y, -x)^T$
  -->
 <IMG
- WIDTH="107" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
+ WIDTH="108" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
  SRC="step-18.data/intro/img72.png"
- ALT="$ \Delta\vec u=(y, -x)^T$">, with which <!-- MATH
+ ALT="$ \Delta\vec u=(y, -x)^T$">
+, with which <!-- MATH
  $\varepsilon(\Delta \vec u)=0$
  -->
 <IMG
- WIDTH="75" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
+ WIDTH="77" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
  SRC="step-18.data/intro/img73.png"
- ALT="$ \varepsilon(\Delta \vec u)=0$">). Nevertheless, if the the material was pre-stressed in a certain
+ ALT="$ \varepsilon(\Delta \vec u)=0$">
+). Nevertheless, if the the material was pre-stressed in a certain
 direction, then this direction will be rotated along with the material.  To
 this end, we have to define a rotation matrix <!-- MATH
  $R(\Delta \vec u^n)$
  -->
 <IMG
- WIDTH="60" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
+ WIDTH="61" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
  SRC="step-18.data/intro/img74.png"
- ALT="$ R(\Delta \vec u^n)$"> that
+ ALT="$ R(\Delta \vec u^n)$">
+ that
 describes, in each point the rotation due to the displacement increments. It
 is not hard to see that the actual dependence of <IMG
- WIDTH="15" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
+ WIDTH="17" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
  SRC="step-18.data/intro/img75.png"
- ALT="$ R$"> on <!-- MATH
+ ALT="$ R$">
+ on <!-- MATH
  $\Delta \vec u^n$
  -->
 <IMG
- WIDTH="35" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
+ WIDTH="37" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
  SRC="step-18.data/intro/img39.png"
- ALT="$ \Delta \vec u^n$"> can
+ ALT="$ \Delta \vec u^n$">
+ can
 only be through the curl of the displacement, rather than the displacement
 itself or its full gradient (as mentioned above, the constant components of
 the increment describe translations, its divergence the dilational modes, and
 the curl the rotational modes). Since the exact form of <IMG
- WIDTH="15" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
+ WIDTH="17" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
  SRC="step-18.data/intro/img75.png"
- ALT="$ R$"> is cumbersome, we
+ ALT="$ R$">
+ is cumbersome, we
 only state it in the program code, and note that the correct updating formula
 for the stress variable is then
 <P></P>
 <DIV ALIGN="CENTER"><TABLE CELLPADDING="0" WIDTH="100%" ALIGN="CENTER">
 <TR VALIGN="MIDDLE">
 <TD NOWRAP ALIGN="CENTER"><IMG
- WIDTH="298" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
+ WIDTH="299" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
  SRC="step-18.data/intro/img76.png"
  ALT="$\displaystyle \sigma^n = R(\Delta \vec u^n)^T [\sigma^{n-1} + C \varepsilon (\Delta \vec u^n)] R(\Delta \vec u^n).$"></TD>
 <TD NOWRAP WIDTH="10" ALIGN="RIGHT">
@@ -941,34 +1013,37 @@ sequence of operations on the present mesh:
 A^K_{ij}$
  -->
 <IMG
- WIDTH="103" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
+ WIDTH="105" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
  SRC="step-18.data/intro/img77.png"
  ALT="$ A_{ij} = \sum_K
-A^K_{ij}$"> built up of local contributions on each cell <IMG
- WIDTH="18" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
+A^K_{ij}$">
+ built up of local contributions on each cell <IMG
+ WIDTH="19" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
  SRC="step-18.data/intro/img65.png"
- ALT="$ K$"> with entries
+ ALT="$ K$">
+ with entries
   <P></P>
 <DIV ALIGN="CENTER"><TABLE CELLPADDING="0" WIDTH="100%" ALIGN="CENTER">
 <TR VALIGN="MIDDLE">
 <TD NOWRAP ALIGN="CENTER"><IMG
- WIDTH="170" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
+ WIDTH="171" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
  SRC="step-18.data/intro/img78.png"
- ALT="$\displaystyle A^K_{ij} = (C \varepsilon(\varphi_i), \varepsilon(\varphi_j))_K;$"></TD>
+ ALT="$\displaystyle A^K_{ij} = (C \varepsilon(\varphi_j), \varepsilon(\varphi_i))_K;$"></TD>
 <TD NOWRAP WIDTH="10" ALIGN="RIGHT">
 (21)</TD></TR>
 </TABLE></DIV>
 <BR CLEAR="ALL"><P></P>
 In practice, <IMG
- WIDTH="27" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
+ WIDTH="29" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
  SRC="step-18.data/intro/img79.png"
- ALT="$ A^K$"> is computed using numerical quadrature according to the
+ ALT="$ A^K$">
+ is computed using numerical quadrature according to the
   formula
   <P></P>
 <DIV ALIGN="CENTER"><TABLE CELLPADDING="0" WIDTH="100%" ALIGN="CENTER">
 <TR VALIGN="MIDDLE">
 <TD NOWRAP ALIGN="CENTER"><IMG
- WIDTH="275" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
+ WIDTH="277" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
  SRC="step-18.data/intro/img80.png"
  ALT="$\displaystyle A^K_{ij} = \sum_q w_q [\varepsilon(\varphi_i(\vec x_q)) : C : \varepsilon(\varphi_j(\vec x_q))],$"></TD>
 <TD NOWRAP WIDTH="10" ALIGN="RIGHT">
@@ -976,46 +1051,53 @@ In practice, <IMG
 </TABLE></DIV>
 <BR CLEAR="ALL"><P></P>
 with quadrature points <IMG
- WIDTH="20" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
+ WIDTH="21" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
  SRC="step-18.data/intro/img64.png"
- ALT="$ \vec x_q$"> and weights <IMG
- WIDTH="21" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
+ ALT="$ \vec x_q$">
+ and weights <IMG
+ WIDTH="23" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
  SRC="step-18.data/intro/img63.png"
- ALT="$ w_q$">. We have built these
+ ALT="$ w_q$">
+. We have built these
   contributions before, in step-8 and step-17, but in both of these cases we
   have done so rather clumsily by using knowledge of how the rank-4 tensor <IMG
- WIDTH="16" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
+ WIDTH="17" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
  SRC="step-18.data/intro/img17.png"
  ALT="$ C$">
+
   is composed, and considering individual elements of the strain tensors
   <!-- MATH
  $\varepsilon(\varphi_i),\varepsilon(\varphi_j)$
  -->
 <IMG
- WIDTH="83" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
+ WIDTH="84" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
  SRC="step-18.data/intro/img81.png"
- ALT="$ \varepsilon(\varphi_i),\varepsilon(\varphi_j)$">. This is not really
+ ALT="$ \varepsilon(\varphi_i),\varepsilon(\varphi_j)$">
+. This is not really
   convenient, in particular if we want to consider more complicated elasticity
   models than the isotropic case for which <IMG
- WIDTH="16" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
+ WIDTH="17" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
  SRC="step-18.data/intro/img17.png"
- ALT="$ C$"> had the convenient form
+ ALT="$ C$">
+ had the convenient form
   <!-- MATH
- $c_{ijkl}  = \lambda \delta_{ij} \delta_{kl} + \mu (\delta_{ik} \delta_{jl}
+ $C_{ijkl}  = \lambda \delta_{ij} \delta_{kl} + \mu (\delta_{ik} \delta_{jl}
 + \delta_{il} \delta_{jk})$
  -->
 <IMG
- WIDTH="235" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
+ WIDTH="241" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
  SRC="step-18.data/intro/img82.png"
- ALT="$ c_{ijkl} = \lambda \delta_{ij} \delta_{kl} + \mu (\delta_{ik} \delta_{jl}
-+ \delta_{il} \delta_{jk})$">. While we in fact do not use a more complicated
+ ALT="$ C_{ijkl} = \lambda \delta_{ij} \delta_{kl} + \mu (\delta_{ik} \delta_{jl}
++ \delta_{il} \delta_{jk})$">
+. While we in fact do not use a more complicated
   form than this in the present program, we nevertheless want to write it in a
   way that would easily allow for this. It is then natural to introduce
   classes that represent symmetric tensors of rank 2 (for the strains and
   stresses) and 4 (for the stress-strain tensor <IMG
- WIDTH="16" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
+ WIDTH="17" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
  SRC="step-18.data/intro/img17.png"
- ALT="$ C$">). Fortunately, deal.II
+ ALT="$ C$">
+). Fortunately, deal.II
   provides these: the <TT>SymmetricTensor&lt;rank,dim&gt;</TT> class template
   provides a full-fledged implementation of such tensors of rank <TT>rank</TT>
   (which needs to be an even number) and dimension <TT>dim</TT>.
@@ -1023,54 +1105,63 @@ with quadrature points <IMG
 <P>
 What we then need is two things: a way to create the stress-strain rank-4
   tensor <IMG
- WIDTH="16" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
+ WIDTH="17" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
  SRC="step-18.data/intro/img17.png"
- ALT="$ C$"> as well as to create a symmetric tensor of rank 2 (the strain
+ ALT="$ C$">
+ as well as to create a symmetric tensor of rank 2 (the strain
   tensor) from the gradients of a shape function <IMG
- WIDTH="19" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
+ WIDTH="20" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
  SRC="step-18.data/intro/img83.png"
- ALT="$ \varphi_i$"> at a quadrature
+ ALT="$ \varphi_i$">
+ at a quadrature
   point <IMG
- WIDTH="20" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
+ WIDTH="21" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
  SRC="step-18.data/intro/img64.png"
- ALT="$ \vec x_q$"> on a given cell. At the top of the implementation of this
+ ALT="$ \vec x_q$">
+ on a given cell. At the top of the implementation of this
   example program, you will find such functions. The first one,
   <TT>get_stress_strain_tensor</TT>, takes two arguments corresponding to
   the Lam&#233; constants <IMG
- WIDTH="12" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
+ WIDTH="14" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
  SRC="step-18.data/intro/img84.png"
- ALT="$ \lambda$"> and <IMG
- WIDTH="13" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
+ ALT="$ \lambda$">
+ and <IMG
+ WIDTH="14" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
  SRC="step-18.data/intro/img85.png"
- ALT="$ \mu$"> and returns the stress-strain tensor
+ ALT="$ \mu$">
+ and returns the stress-strain tensor
   for the isotropic case corresponding to these constants (in the program, we
   will choose constants corresponding to steel); it would be simple to replace
   this function by one that computes this tensor for the anisotropic case, or
   taking into account crystal symmetries, for example. The second one,
   <TT>get_strain</TT> takes an object of type <TT>FEValues</TT> and indices
   <IMG
- WIDTH="9" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
+ WIDTH="10" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
  SRC="step-18.data/intro/img86.png"
- ALT="$ i$"> and <IMG
- WIDTH="11" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
+ ALT="$ i$">
+ and <IMG
+ WIDTH="12" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
  SRC="step-18.data/intro/img68.png"
- ALT="$ q$"> and returns the symmetric gradient, i.e. the strain,
+ ALT="$ q$">
+ and returns the symmetric gradient, i.e. the strain,
   corresponding to shape function <!-- MATH
  $\varphi_i(\vec x_q)$
  -->
 <IMG
- WIDTH="48" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
+ WIDTH="49" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
  SRC="step-18.data/intro/img87.png"
- ALT="$ \varphi_i(\vec x_q)$">, evaluated on the cell
+ ALT="$ \varphi_i(\vec x_q)$">
+, evaluated on the cell
   on which the <TT>FEValues</TT> object was last reinitialized.
 
 <P>
 Given this, the innermost loop of <TT>assemble_system</TT> computes the
   local contributions to the matrix in the following elegant way (the variable
   <TT>stress_strain_tensor</TT>, corresponding to the tensor <IMG
- WIDTH="16" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
+ WIDTH="17" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
  SRC="step-18.data/intro/img17.png"
- ALT="$ C$">, has
+ ALT="$ C$">
+, has
   previously been initialized with the result of the first function above):
   <PRE>
 for (unsigned int i=0; i&lt;dofs_per_cell; ++i)
@@ -1101,7 +1192,7 @@ Assembling the local contributions
 <DIV ALIGN="CENTER"><TABLE CELLPADDING="0" WIDTH="100%" ALIGN="CENTER">
 <TR VALIGN="MIDDLE">
 <TD NOWRAP ALIGN="CENTER"><IMG
- WIDTH="331" HEIGHT="72" ALIGN="BOTTOM" BORDER="0"
+ WIDTH="331" HEIGHT="71" ALIGN="BOTTOM" BORDER="0"
  SRC="step-18.data/intro/img88.png"
  ALT="\begin{gather*}\begin{split}f^K_i &amp;= (\vec f, \varphi_i)_K -(\sigma^{n-1},\varep...
 ...gma^{n-1}_q : \varepsilon(\varphi_i(\vec x_q)) \right\} \end{split}\end{gather*}"></TD>
@@ -1111,18 +1202,20 @@ Assembling the local contributions
 <BR CLEAR="ALL"><P></P>
 to the right hand side of (<A HREF="#eq:linear-system">17</A>) is equally
   straightforward (note that we do not consider any boundary tractions <IMG
- WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
+ WIDTH="15" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
  SRC="step-18.data/intro/img89.png"
- ALT="$ \vec b$"> here). Remember that we only had to store the old stress in the
+ ALT="$ \vec b$">
+ here). Remember that we only had to store the old stress in the
   quadrature points of cells. In the program, we will provide a variable
   <TT>local_quadrature_points_data</TT> that allows to access the stress
   <!-- MATH
  $\sigma^{n-1}_q$
  -->
 <IMG
- WIDTH="38" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
+ WIDTH="39" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
  SRC="step-18.data/intro/img90.png"
- ALT="$ \sigma^{n-1}_q$"> in each quadrature point. With this the code for the right
+ ALT="$ \sigma^{n-1}_q$">
+ in each quadrature point. With this the code for the right
   hand side looks as this, again rather elegant:
   <PRE>
 for (unsigned int i=0; i&lt;dofs_per_cell; ++i)
@@ -1149,21 +1242,24 @@ for (unsigned int i=0; i&lt;dofs_per_cell; ++i)
  $\vec f(\vec x_q) \cdot \varphi_i(\vec x_q)$
  -->
 <IMG
- WIDTH="96" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
+ WIDTH="97" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
  SRC="step-18.data/intro/img91.png"
- ALT="$ \vec f(\vec x_q) \cdot \varphi_i(\vec x_q)$">, we have made use of the fact that for the chosen finite element, only
+ ALT="$ \vec f(\vec x_q) \cdot \varphi_i(\vec x_q)$">
+, we have made use of the fact that for the chosen finite element, only
   one vector component (namely <TT>component_i</TT>) of <IMG
- WIDTH="19" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
+ WIDTH="20" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
  SRC="step-18.data/intro/img83.png"
- ALT="$ \varphi_i$"> is
+ ALT="$ \varphi_i$">
+ is
   nonzero, and that we therefore also have to consider only one component of
   <!-- MATH
  $\vec f(\vec x_q)$
  -->
 <IMG
- WIDTH="39" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
+ WIDTH="41" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
  SRC="step-18.data/intro/img92.png"
- ALT="$ \vec f(\vec x_q)$">.
+ ALT="$ \vec f(\vec x_q)$">
+.
 
 <P>
 This essentially concludes the new material we present in this function. It
@@ -1188,9 +1284,10 @@ This essentially concludes the new material we present in this function. It
  $\Delta \vec u^n$
  -->
 <IMG
- WIDTH="35" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
+ WIDTH="37" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
  SRC="step-18.data/intro/img39.png"
- ALT="$ \Delta \vec u^n$"> computed before, we update the stress values in all quadrature points
+ ALT="$ \Delta \vec u^n$">
+ computed before, we update the stress values in all quadrature points
   according to (<A HREF="#eq:stress-update">18</A>) and (<A HREF="#eq:stress-update+rot">20</A>),
   including the rotation of the coordinate system.
 
@@ -1260,7 +1357,7 @@ elastic energy
 <DIV ALIGN="CENTER"><TABLE CELLPADDING="0" WIDTH="100%" ALIGN="CENTER">
 <TR VALIGN="MIDDLE">
 <TD NOWRAP ALIGN="CENTER"><IMG
- WIDTH="310" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
+ WIDTH="311" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
  SRC="step-18.data/intro/img93.png"
  ALT="$\displaystyle E(\vec u) = (\varepsilon(\vec u), C\varepsilon(\vec u))_{\Omega} - (\vec f, \vec u)_{\Omega} - (\vec b, \vec u)_{\Gamma_N},$"></TD>
 <TD NOWRAP WIDTH="10" ALIGN="RIGHT">
@@ -1272,7 +1369,7 @@ subject to the constraint
 <DIV ALIGN="CENTER"><TABLE CELLPADDING="0" WIDTH="100%" ALIGN="CENTER">
 <TR VALIGN="MIDDLE">
 <TD NOWRAP ALIGN="CENTER"><IMG
- WIDTH="86" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
+ WIDTH="88" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
  SRC="step-18.data/intro/img94.png"
  ALT="$\displaystyle f(\sigma(\vec u)) \le 0$"></TD>
 <TD NOWRAP WIDTH="10" ALIGN="RIGHT">
@@ -1315,7 +1412,7 @@ Incompressibility is characterized by Poisson's ratio
 <DIV ALIGN="CENTER"><TABLE CELLPADDING="0" WIDTH="100%" ALIGN="CENTER">
 <TR VALIGN="MIDDLE">
 <TD NOWRAP ALIGN="CENTER"><IMG
- WIDTH="100" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
+ WIDTH="101" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
  SRC="step-18.data/intro/img95.png"
  ALT="$\displaystyle \nu = \frac{\lambda}{2(\lambda+\mu)},$"></TD>
 <TD NOWRAP WIDTH="10" ALIGN="RIGHT">
@@ -1326,23 +1423,27 @@ where <!-- MATH
  $\lambda,\mu$
  -->
 <IMG
- WIDTH="29" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
+ WIDTH="30" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
  SRC="step-18.data/intro/img96.png"
- ALT="$ \lambda,\mu$"> are the Lam&#233; constants of the material.
+ ALT="$ \lambda,\mu$">
+ are the Lam&#233; constants of the material.
 Physical constraints indicate that <!-- MATH
  $-1\le \nu\le \tfrac 12$
  -->
 <IMG
- WIDTH="85" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
+ WIDTH="86" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
  SRC="step-18.data/intro/img97.png"
- ALT="$ -1\le \nu\le \tfrac 12$">. If <IMG
- WIDTH="12" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
+ ALT="$ -1\le \nu\le \tfrac 12$">
+. If <IMG
+ WIDTH="13" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
  SRC="step-18.data/intro/img98.png"
  ALT="$ \nu$">
+
 approaches <IMG
- WIDTH="13" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
+ WIDTH="15" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
  SRC="step-18.data/intro/img99.png"
- ALT="$ \tfrac 12$">, then the material becomes incompressible. In that
+ ALT="$ \tfrac 12$">
+, then the material becomes incompressible. In that
 case, pure displacement-based formulations are no longer appropriate for the
 solution of such problems, and stabilization techniques have to be employed
 for a stable and accurate solution. The book and paper cited above give
@@ -1366,16 +1467,16 @@ you wish. The main complication one has to overcome is that one has to
 transfer the data that is stored in the quadrature points of the cells of the
 old mesh to the new mesh, preferably by some sort of projection scheme. This
 is only slightly messy in the sequential case; in fact, the functions
-<tt>FETools::get_projection_from_quadrature_points_matrix</tt> will do
-the projection, and the <tt>FiniteElement::get_restriction_matrix</tt> and
-<tt>FiniteElement::get_prolongation_matrix</tt> functions will do the
-transfer between mother and child cells. However, it becomes complicated once
-we run the program in parallel, since then each process only stores this data
-for the cells it owned on the old mesh, and it may need to know the values of
-the quadrature point data on other cells if the corresponding cells on the new
-mesh are assigned to this process after subdividing the new mesh. A global
-communication of these data elements is therefore necessary, making the entire
-process a little more unpleasant.
+<TT>FETools</TT> <TT>::</TT> <TT>get_projection_from_quadrature_points_matrix</TT> will do
+the projection, and the <TT>FiniteElement</TT> <TT>::</TT> <TT>get_restriction_matrix</TT> and
+<TT>FiniteElement</TT> <TT>::</TT> <TT>get_prolongation_matrix</TT> functions will do the
+transfer between mother and child cells. However, it becomes complicated
+once we run the program in parallel, since then each process only stores this
+data for the cells it owned on the old mesh, and it may need to know the
+values of the quadrature point data on other cells if the corresponding cells
+on the new mesh are assigned to this process after subdividing the new mesh. A
+global communication of these data elements is therefore necessary, making the
+entire process a little more unpleasant.
 
 <P>
 
@@ -1411,4 +1512,3 @@ although this is already done in the distributed version of the Makefile.
 Conversely, if you want to run the program in 2d (after making the necessary
 changes to accommodate for a 2d geometry), you have to change the Makefile
 back to allow for 2d.
-
diff --git a/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro.pdf b/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro.pdf
index 05a5e2e4b849c8de8df314e250f7b23b883aadd2..a5b88b1ae765bd19448720d3c351bec78091db76 100644
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diff --git a/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img1.png b/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img1.png
index 323baaa448afda66753d32a9dca198a63bf95818..4f85ec90841b045c59d6c40ea663378127ee7d25 100644
GIT binary patch
delta 1130
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delta 1114
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diff --git a/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img10.png b/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img10.png
index 2fea50fed4ffd71d6622f542459a64359396520d..d4f762bbfc5da55038ffb03d59264decb9dd8c8f 100644
GIT binary patch
delta 362
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delta 360
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diff --git a/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img11.png b/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img11.png
index 59c33a6e6fb4d20a6945719d32e807297462b82c..edf440bcf94345f395da0d6045641078e82f1cf1 100644
GIT binary patch
delta 356
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delta 359
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diff --git a/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img12.png b/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img12.png
index e09962d3d1926adc14278ef35fa9537ca696644c..897795f8bcb0b9afb4afb1e8e0a86f3df7581c47 100644
GIT binary patch
delta 494
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delta 511
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diff --git a/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img13.png b/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img13.png
index fd918c6a5520a2d5078460a1d5e493e592049dfd..e24e3a6c2975011a9b75ac31bfc856f8d5e50ede 100644
GIT binary patch
delta 396
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delta 406
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diff --git a/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img14.png b/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img14.png
index f7e973bd1142191ea57355d9ed2ca324a036e0e4..18f848a3b58e25bcb2c731523e7b066f010f3964 100644
GIT binary patch
delta 442
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delta 438
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diff --git a/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img15.png b/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img15.png
index ca804b7cf443f6aa3dbc38e254eba53771b60b11..646de73fd450c3dfae6f89a4576f107698491954 100644
GIT binary patch
literal 123
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literal 118
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diff --git a/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img16.png b/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img16.png
index 448517fb5417b92e67ea41dfd2f205ccf8ce91f4..abfc0473d396a6a44c371e6fce40adbcb16ff643 100644
GIT binary patch
delta 633
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delta 624
zcmV-$0+0Q;1+N7miBL{Q4GJ0x0000DNk~Le0001)0000Z1Oos70Rkk243QyBe=SKw
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diff --git a/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img17.png b/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img17.png
index 2897e02957e9a42cbe7a733dc1fe7144e05275e7..71e902470bcb9e5773c715130569d2bf08b3e331 100644
GIT binary patch
delta 151
zcmcc5c%M<RGr-TCmrII^fq{Y7)59eQNDBfn9}6=B1EbH8TY?i619LfMCMPsBG4t?T
zmXw$wc~B-TPvGP=hRGs{32c+(C1fNfFs?ty%+|)u;}FUyzzAe@U*lQPu<_adL!1f5
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delta 151
zcmcc5c%M<RGr-TCmrII^fq{Y7)59eQNDBZl9}6=B1LI=0jrtQ619L0pBquO5GqABm
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BE3p6o

diff --git a/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img18.png b/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img18.png
index 044dc1e35e9c767b12d1b785177e4c3e8d09d59f..4044e4d13b61f776cacbb2c0688ffd74462413f7 100644
GIT binary patch
delta 148
zcmX@lc%4zPGr-TCmrII^fq{Y7)59eQL<2D&3o`=)V`13t@`;K*S)raTjv*W~lM@mi
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delta 140
zcmcc4c%D(QGr-TCmrII^fq{Y7)59eQNOJ=*9}6=B17nTHX@iN1K1sfwE{-7;bCMGh
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diff --git a/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img19.png b/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img19.png
index 9333d20b5a54b36597bbc9de37d7b5e2b8d60952..bee30fa41fad1f33e90bf7d3e053c9a506c656ba 100644
GIT binary patch
delta 461
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Di~G;B

delta 444
zcmV;t0Ym<c1pEUbiBL{Q4GJ0x0000DNk~Le000100000W1Oos70p>FqjgcWte|kwo
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diff --git a/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img2.png b/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img2.png
index cda8ace6b06bd9b1dd027def5cb5b329d735780e..dbf248687625808f9c76fec0538dc2942bfe3fd1 100644
GIT binary patch
delta 190
zcmcb|c!yE7Gr-TCmrII^fq{Y7)59eQNDBZl9}6=B1LI=0jru^2!9-P!dKDEF2?+@v
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delta 192
zcmcb^c#l!FGr-TCmrII^fq{Y7)59eQNb>_R9}6=B17qppY%d^3ccQ9By@Z4W4-XHJ
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diff --git a/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img20.png b/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img20.png
index 1612593773b87b3f13fcb91b451de91704ba952c..b17e0d9b2e8fdbebb91f9917b28516b6bfd12065 100644
GIT binary patch
delta 592
zcmV-W0<Zo31datEiBL{Q4GJ0x0000DNk~Le0001K0000a1Oos70S|3CEs-Hhe*z3i
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delta 575
zcmV-F0>J%_1^omeiBL{Q4GJ0x0000DNk~Le0001I0000a1Oos70THALo{=F-e*ybR
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N002ovPDHLkV1icT4+Q`K

diff --git a/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img21.png b/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img21.png
index e24eea5e62d9ff88b8f377469b947bcd886d8f64..59f19b94768246b458944fd8a051a87fabfb4e92 100644
GIT binary patch
delta 272
zcmV+r0q_300@4B@iBL{Q4GJ0x0000DNk~Le0000d0000U1Oos70V@A0^^qY=f6z%p
zK~yM_V_*OR4ju+nP{6<-#sOtN-~*8k3<d%W*uen?ZU#1n4?xyD1_cH_9IDX40|o|m
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W5FcgY1>y4m0000<MNUMnLSTYCbX;x#

delta 248
zcmV<U00;ll0=fbriBL{Q4GJ0x0000DNk~Le0000c0000U1Oos70mVH*%aI{Wf4E6R
zK~#90V_*OS0S07X0K^_}9tW6YV)(#-4Qv34^E31TS^NwQ3<@Bj1gr{C0VC944WK@t
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diff --git a/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img22.png b/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img22.png
index 32648dfb1bdddb8ce903825426ac1736317a0dc3..51bc83c6dd9bbe2bc34736c00e26ca6f9dba2185 100644
GIT binary patch
delta 150
zcmZ3;xR6n?Gr-TCmrII^fq{Y7)59eQM1wF3GXn$T_d_RdPE-`hX=!Q6$;k-`2{AA*
zkdTnz;o$))xjVr#6i6|a1o;IsI6S+N2IS~@x;Tb#%uG%=z!V`NaU<c)icp6p=Gdca
uT6xZ_2`FPSQ(n-ZDVP>u)RLsfAjEL0lliA>aLjw4P6kg`KbLh*2~7Z77ApAw

delta 150
zcmZ3;xR6n?Gr-TCmrII^fq{Y7)59eQNb`W$EX)iHj1mlso=;R1$pM0dgoKcg5DyOz
z6%`c;2??N*rWZ#-ffQp&kY6x^!?PP{K#rcLi(^Q|oa6)thA@f4EQ)5?jLcREajYW7
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diff --git a/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img23.png b/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img23.png
index 197ba5e46331ab7a26fcee467fa0fee8303e2791..37de84a542fed4e9ef234d9ee4423b33ed14c714 100644
GIT binary patch
delta 463
zcmV;=0Wki81djwEiBL{Q4GJ0x0000DNk~Le0001E0000W1Oos70fXM_@{u7-e~n2*
zK~y-6?UOxD!$1&)pJO{Va*{QoA)Swqf`-l#2q7Vq9Ki=b!lFq-;gnR#4G;x2z5ys4
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FV1lU{(qI4p

delta 450
zcmV;z0X_bY1cC%1iBL{Q4GJ0x0000DNk~Le0001C0000W1Oos70f#F)&ygWae}G9u
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delta 355
zcmV-p0i6E(0{Q|aiBL{Q4GJ0x0000DNk~Le0000m0000W1Oos70nz=|xc~qFFp(u9
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diff --git a/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img34.png b/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img34.png
index 561079e9c85c9d34adcee3b10c8f46b5d2496b30..96f95c6216c3ffa8c8ea050842c4a31737107359 100644
GIT binary patch
delta 403
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delta 402
zcmV;D0d4-&1JeT`iBL{Q4GJ0x0000DNk~Le0000{0000W1Oos70q@wk_mLq?e^E(9
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diff --git a/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img35.png b/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img35.png
index 4585efe54a00adde19d6a7905561ce9faa9c3265..404f319a009179ac2536bc8221a444d9723c1e84 100644
GIT binary patch
delta 303
zcmdnPbeKuCGr-TCmrII^fq{Y7)59eQNGk!c0t+((1LLP<?Kwb>!9-R0dJhi|8ygz~
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delta 295
zcmX@iw1-KxGr-TCmrII^fq{Y7)59eQNGk%d0t+((1Eb_bn|vTgccQ9%y^W2Hfq{XF
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diff --git a/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img36.png b/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img36.png
index bdab1750ca3634bc9e7d0f8014ce5524c55f115e..e65e53a072f05d081ab2b5ea46b2ef5897621f72 100644
GIT binary patch
delta 168
zcmX@Yc!W{4Gr-TCmrII^fq{Y7)59eQNb`Z%EX)iHj51$~ZUH$46IE5K3=9lZR8%A+
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delta 168
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diff --git a/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img37.png b/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img37.png
index 0161316c0442c2ed10298e51baeb62093b678198..71f20f386cd624279658eb4fd6f90eccf7e54bab 100644
GIT binary patch
delta 385
zcmV-{0e=3;1HuC#iBL{Q4GJ0x0000DNk~Le0001L0000V1Oos70gC5!K#?I#e?Un@
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delta 392
zcmV;30eAkw1IYs+iBL{Q4GJ0x0000DNk~Le0001K0000V1Oos70b$V2Ly;j&e@96~
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diff --git a/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img38.png b/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img38.png
index 26745c1d616b80a28f5f1567db4b61aaced9f35c..3ccaa26cd98955269d4a97ec16d62507daeb8893 100644
GIT binary patch
delta 645
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delta 630
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diff --git a/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img39.png b/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img39.png
index 614a8feb42ec300f037c4634746ff090c6fbc01f..7309f7ecc1110a1741c0cc8d0cff28b8d5dc3fa2 100644
GIT binary patch
delta 214
zcmV;{04e{J0+<3JiBL{Q4GJ0x0000DNk~Le0000b0000E1Oos70WIA4Q;{J|f0ju^
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delta 210
zcmV;@04@KR0+a$FiBL{Q4GJ0x0000DNk~Le0000Z0000E1Oos70U*MN6p<lJf09W=
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diff --git a/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img4.png b/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img4.png
index a8d58b909771de0ad3a167419fa464c8c41ef0e2..82a35db95c7cbee35bb7db2adcb79ebb184d55d2 100644
GIT binary patch
delta 407
zcmV;I0cifN1Fi!liBL{Q4GJ0x0000DNk~Le0000{0000W1Oos70q@wk_W%F@Es-T6
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delta 407
zcmV;I0cifN1Fi!liBL{Q4GJ0x0000DNk~Le0000_0000W1Oos70oK0=tN;K2Fp(u9
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diff --git a/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img40.png b/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img40.png
index 6a5f66328c37267f8230fa847cff11e8a9636fb5..42ff48a26072041bf497fed87faae5e0fbdd6163 100644
GIT binary patch
delta 508
zcmV<Y0R#TG1iS<xiBL{Q4GJ0x0000DNk~Le0001N0000W1Oos70dm!_e~}?ff4WIT
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delta 503
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diff --git a/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img41.png b/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img41.png
index 2d4c288be170a78d3e3d2dae7e371c00b6dcf1bc..8a5fc6c6ad1cf9f4bd1e0ca9ecd01d73a9f1d4b2 100644
GIT binary patch
literal 549
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literal 568
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diff --git a/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img42.png b/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img42.png
index c63be1b45d7f9ea6deacb8ac019a97cbd4a97dad..24f793de1a7560d6f3855b5008a5641753525f82 100644
GIT binary patch
delta 346
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delta 343
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diff --git a/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img43.png b/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img43.png
index e8ca6ae9755e6ace0ba6e24bddeec35e604e2ebc..457a2eea244a08900c0871f37dd7361cb55fd0e4 100644
GIT binary patch
delta 403
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delta 399
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diff --git a/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img44.png b/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img44.png
index c24306e1951b2ef84d6d1355fc22fafa34021376..71e35110396bc1bfc6acf74962c6a91b2c0ce64e 100644
GIT binary patch
delta 637
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delta 655
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diff --git a/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img45.png b/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img45.png
index 1afc2be6154284b2c0be301236deb068caf9e728..660e1f7a9e12d890568f8a11c41641bddca66bc5 100644
GIT binary patch
delta 512
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delta 512
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diff --git a/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img46.png b/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img46.png
index 3b8e2fd342d9978cb4e49a0ad69d03cf043ff8a7..4752bb803a99697724e5e358afc1d1db33229deb 100644
GIT binary patch
delta 596
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delta 585
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diff --git a/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img47.png b/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img47.png
index db799d55ac5a3a27c95d78a2a7bf11742f5bf007..2ce876f00fb3e795fa025caf3762ec10a635c8f2 100644
GIT binary patch
delta 640
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delta 650
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diff --git a/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img48.png b/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img48.png
index b8450755fa089892952ca6b1a75e1551ecff58ba..6208f147f1f78b885cd5642e141cfa3f9cd60573 100644
GIT binary patch
delta 609
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delta 606
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diff --git a/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img49.png b/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img49.png
index 7606d6a664bdee8cf10577a9ee42f087535bd726..a7412b9f18985044aebb8962e80bf496cc98fe2c 100644
GIT binary patch
delta 1273
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delta 1277
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diff --git a/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img5.png b/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img5.png
index fd0a2608e918dd23b7c0d02ff253cd301f638c22..095ea468290eebeb1fdd17353d49532d7244136f 100644
GIT binary patch
delta 204
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delta 186
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diff --git a/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img50.png b/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img50.png
index dc406d64c048f78eee5dbc0f43cfb8ab42f05c85..a1369cbfc848e350d06382d788e1bf3610217bd1 100644
GIT binary patch
delta 2928
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diff --git a/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img51.png b/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img51.png
index d379718c151b6496990d6563b2ea6c30803588b0..11b7c77c301b7e144b45bca60455c984bb3ba6f2 100644
GIT binary patch
delta 204
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delta 198
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diff --git a/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img52.png b/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img52.png
index ffcc41d573c3c4c9b38aace6b0c7f24d7bcaf77d..b4019faf2d985217e5a7d58da3d38e05486ee998 100644
GIT binary patch
delta 181
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delta 180
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diff --git a/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img53.png b/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img53.png
index 4926fc81f5511118f27edb07457712591121c2ea..964a5b666ac970cb709aaecc7abba56eda310986 100644
GIT binary patch
delta 741
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delta 732
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diff --git a/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img54.png b/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img54.png
index df496ba11e3a94cec737f960c4d52c7fd38c6396..48e64e60b223a40f5578437574cce0b8165fdba3 100644
GIT binary patch
delta 269
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delta 265
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diff --git a/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img55.png b/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img55.png
index 7f66221be6a83693517a7ba59fded66da1bbde3b..6b14e28499b73683a2b694d28b6bb1df27a837cb 100644
GIT binary patch
delta 225
zcmV<703QFI0;2*UiBL{Q4GJ0x0000DNk~Le0000S0000U1Oos70lMr{I*}nvf1yc4
zK~xx(V_*OReg-&T0b&KP*nbfDf#m=L8URc1GbDo)I-pCU0W}6Th^Yw;OkhSP1IsT0
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b(MSLQ(NG*hBpnno00000NkvXXu0mjfRiaDI

delta 220
zcmV<203-jS0-gdPiBL{Q4GJ0x0000DNk~Le0000R0000U1Oos70a!3dLy;j&f1F7~
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diff --git a/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img56.png b/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img56.png
index 2fa4b0cea92f8d733d0d09e43d835b11769866f3..1ea0e6a1b744e368c6b6df27bf25d79a361995cd 100644
GIT binary patch
delta 174
zcmV;f08#(-0rdePiBL{Q4GJ0x0000DNk~Le0000d0000G1Oos70TA^|g^?jqe;Acx
zU;qOF2xY(k1-x(;9B^O?K>(v4|Njpl23r7J?7{;aiqQaAA49&t|Nl@Xi#SyDzy`P?
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delta 174
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diff --git a/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img57.png b/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img57.png
index adad427a4bdc03c4673b0d49ad9f6fc8dd8fd54c..0308bdfb3bd4f925205bb38c76c4f2065b1888a5 100644
GIT binary patch
delta 172
zcmV;d08{_t0qy}IiBL{Q4GJ0x0000DNk~Le0000N0000H1Oos70kc{f7?B}Ne{4xa
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delta 160
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diff --git a/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img58.png b/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img58.png
index 3038f9623e4fd92a94b12b48e94b876cfeb99b42..01cd7abc69762b295b62b167fb68fc700dd66b08 100644
GIT binary patch
delta 201
zcmV;)05<>m0gD15iBL{Q4GJ0x0000DNk~Le0000f0000U1Oos70W>xmMv);*e~C#%
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delta 183
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diff --git a/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img59.png b/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img59.png
index 1df25e7f516fbad2ae094fe88783c229751b2130..839a8a8a29a41b79f25287e5969c50e63c644845 100644
GIT binary patch
delta 634
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delta 622
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diff --git a/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img6.png b/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img6.png
index ec84774d14d7b9f0a6f92a8c092ab650c061ca47..d704ea28ab897a5d796edd2fca14275007e67428 100644
GIT binary patch
literal 171
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literal 172
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diff --git a/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img60.png b/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img60.png
index 458136f56fc0f616f9dcee9a8812373ff4a2e0d6..f7daf45ebb1ad9d948b3a2588f80fe2deb298bbd 100644
GIT binary patch
delta 357
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delta 343
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diff --git a/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img61.png b/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img61.png
index 73ed0355fe9e4c291e702e1bbba63f687bab53b3..d247f1dc675aaba05a8c3d7b16a9c0f90e44f693 100644
GIT binary patch
delta 602
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delta 619
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diff --git a/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img62.png b/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img62.png
index e970b9adf94a9006b6ced2a25fce9135bdc659cf..3b4318b6ca9e35c6369f79d2c65e3564614d230f 100644
GIT binary patch
delta 2103
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h|ANOD<9~?10bqbcgqQul4MzX~002ovPDHLkV1kLm4)Xv2

delta 2167
zcmV--2#ELT5UCL%iBL{Q4GJ0x0000DNk~Le0006D0000q1Oos70fEI<I*}nue+VZ@
zL_t(|ob6goj2uT5em&jO)4TK2W5og@Y&_ydg2=!j3X#A=Vh}%xG`>U;BBY}T2}EQM
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zTBuUJCHT88Ey~B1e(v8L(*V;KqcKO|8$KW0Wys@kNi}g{PmhnF!d4qT1<&Qa4%O%o
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z9$mlquc?9=Cr5d~N@JFwT>0jBI+Lr2Z0(+aA74HC{&k8k7i7J{Ip^WEG6$Puj++>V
zuENjRZCh8jcTn%Hk85&Xt*^y}&FE%Fy?-|bCqJTN*?7j+m@VLx9YEzRTz`ch$;Fa4
z`db4Jeh*`-H#xbzuQtvbO^={U@h+tP;10ae-x@dt4+8v!liM>xz3+@chE&=Nw9(&6
tuvg+MJ0t1dI8Jr_<b1Q7V~!6E{{{KsN4|(UCtv^o002ovPDHLkV1kZ4Dyskh

diff --git a/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img63.png b/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img63.png
index e5b2ae831db021145f355a171ea0a0101d4c724d..c5a2088762f814399473fa33b41da5b1b9de7762 100644
GIT binary patch
delta 192
zcmaFE*u<pR8Q|y6%O%Cdz`(%k>ERLtq{V?)j)j?lfzgR)#o399KJ^WrE{-7*Q<D>b
zAjP49jV<LvHRFt5|Nq;^bewN!Y?NH1!=Tru!_Rt#on?WJWr?N|1NY%}W`!yzrW>~R
z?^voFc=U(wMocI7ANEH6Be!quZ%}R&f5vpJO@@tc29Nw<_O`UPe~}4%w|Bp?XRG1r
r7L>C5=jUM7#-d%={Ga247$bxBBwZG9xy46-PGj(N^>bP0l+XkK!KXmy

delta 169
zcmZo-dc&yL8Q|y6%O%Cdz`(%k>ERLtq(y;PmW7#tf$=~tSKLHJpZY9M7srr_ImrnL
z2@jYav9WPnNOWNO!^R_VfYGHuCBbV!6Sp|af;0|+pf0uuIh7`jbOZNUy{wNmaVJb#
zu=NOY-+Z3LfM7`(D+#%Ss&+*p23j8fSfX$L|MM@cjr|T+!O4GqEu1myHH#S;OjZeB
Uzj2ny0_X+?Pgg&ebxsLQ0IFCuVE_OC

diff --git a/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img64.png b/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img64.png
index 0b0d4f6e5816a6f5328c0419c62981eeb5d32957..4d1fcb84bde317dc351b894fa0a713462f70ac5f 100644
GIT binary patch
delta 217
zcmaFP_={1oGr-TCmrII^fq{Y7)59eQNQ(lo91Al81Ebr|iVqVN#n~z<DspmiCfZ5V
zZ)Z2}07^5K1o;IsI6S+N2IN$Gx;TbNOifMz0=7p?Y#bg54oo_{ObNg4?k+Dd<Xa$+
zT*bJ_Xu%(5Hj@K<!3Uo==(%#(L@-=qPt&hBz-iX;k!gmsgTw3H<tO}(a{sueyP}%)
z@rJ#(IHo7WedKxZM_l+omc+Ha$vci@sxnMpW8G-bIM-wLhuva4atsVsUYZ-27k}>t
Px`V;f)z4*}Q$iB}c7;nG

delta 198
zcmeyx_?%I(Gr-TCmrII^fq{Y7)59eQNQ(fmEDJLO1Ec=>#Ds~8;%qrNISB~~6YV7G
zKlV+s21+xQ1o;IsI6S+N2IORTx;TbZ%t;0+dBF6Dfz9B?0S0CnaW07qjLIDe2L;?%
zYnTF#F*0!l`rPBW_LTP-i@yeg^>f7;$NicND-P}sfAd|;;pVRGq6vp$c1lZ1{J!PL
wHLqZA^?}nHIMfdR+rzl7@*NYK5hKH)7$K4AEGty*11)9nboFyt=akR{0I+*O;Q#;t

diff --git a/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img65.png b/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img65.png
index 0dd0f4f9459a822a0be72f42b7193c1ff8d7f332..f60a2bde1eeca59593496ce374c46ff0d26851c7 100644
GIT binary patch
delta 204
zcmaFJ_<~WfGr-TCmrII^fq{Y7)59eQNDBio9}6=B1EYr_m(D~*wR!^s0~Hk&2?+@v
z9v+~iGvof<K#H*>$S;_|;n|HeASct)#W93qW^w`$q%}0KGx6}$1emEaGyi5~W6NV>
z(I{XLs_Eh7S<w*N!0Yj8L&J?datf1r#a+w{L>H_~iTIw!czU<Hz-MuT4sHjRw>+~F
yxxzHRII%{`8x<(Uux!3@Z*TF3>g^4Uj10G42(DP|{AvNvRt8U3KbLh*2~7Z*Pdm{7

delta 197
zcmaFC_>fVtGr-TCmrII^fq{Y7)59eQNDBcm9}6=B1LN|~i9!<<)#`0*Y*bWKBqStw
zczA%4+jiS^0x8ClAirP+hi5m^fSe>x7srr_Imrn?kleuF#>Q4AX3#x%V&nG4#)FJn
z2M=(E9XfZsfvrMP%Hh!&g|d&V0+o)uK8sdAx%Iuv@%c1{j-6eNs*F0v{zP~&YE`#9
sW@<@IKVTqzrlY!AdgjkN+H7nLKZONs%<KP71X{=7>FVdQ&MBb@0CiYEh5!Hn

diff --git a/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img66.png b/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img66.png
index abb9da7e04667f7b2befdfac545af143b46e78c0..25ac13b2fbf024bdcf7493cb4895c77cd41e6dee 100644
GIT binary patch
delta 479
zcmV<50U-X71fK*UiBL{Q4GJ0x0000DNk~Le000100000W1Oos70p>FqjgcWtf1OE0
zK~y-6?NqT&!$1suY0~y+3(3I11o?y@ejrE)x;5epx-y{l6OI9it(h2LVBiN%Ffmc!
z1IiyzSQuDtKuFL+uybhu(Mkvy7<h7>bNuY{*_Q$ts+b4?D=GsHAaBOFJqXuwH1pia
zNj{*+s=%QH%f}i&+Z=vLKMCk}f7$&nCY_8zpH$0(V#7g5`kb~1T<EmojYU%Z8LlBx
zHtl|WK<i+6w<4iTV@i24j*g}f|G27ep^&d4R#K#Eg_=)~*}icJZXq)Q?xS2Xq%w6F
zl3MN^L6d_{uMFSX2W+;}x1%9aKLQKWA-}Cc=`CqmXOc7MM&KSbblC{=f6AI%foJ{J
zk^eHBCMh8^Ykp@)dNuc2G0O;bRx6LANFJRdb1zRY9U|tgZgI>EG-5OoC(#wux~K+j
zqB;W;tXK#acjj9OQ6x_S*L*lM!qVU@ORNngO|H$*T8g*}IoCdU06KeQ^izS|dkV1)
z^b*1ln=dW1uZY|Pr^$?eHAvT~&5~i<zlXV8;yF%_UVn3}f94j`lcS>{JeGfCcm<%1
VWm+e{C({4`002ovPDHLkV1jX8%1!_P

delta 465
zcmV;?0WSWZ1d#+GiBL{Q4GJ0x0000DNk~Le0000~0000W1Oos70SWPPvymZ8e~(E-
zK~#90<x@XP!$1`OB~6;xq$c2^IM`7rh_h2h5uyDC2D+Dm;wXocf}$Ux;1|f?u0=mU
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zU%_0^+{w<RJ|}h|NRV>sC=kw7fAVA8!c%NXntZen0nHEy6UYPz&`VV5A$MV*3ON9L
zTn<FczT9DkNYxmAzt7);m`Js$k~%skW=r^dj`@PBz^dX0q0L$wO{zMe)eoR%Yuts(
zs}GkHMy|y!)HEcll27TXixz8J-EDO*(6_8n)>$;7TyWSTrfz>0hqTO5e|9h)+Vp^&
zcw${<(r^WB>y6yFr6zsyDN>gSIC~etCIuDN2v#Z^DX#DUydWLB!-QRTm{4g8x+Mw<
z?8OKqZgeCHyzyMqa=?U^7EP+5Jeqa&j(S*m6Y8P!+o`Ab@FJ|G3ZguGOm)(0q_18o
z2OdS<XJVL1aVT}oE>7u>Cq;_#5!8yl$Glgb_-}QJ_Wy?u=#XE67kG3T00000NkvXX
Hu0mjfs|?SJ

diff --git a/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img67.png b/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img67.png
index cc2445bc1c127c8fdee13bebc8140f19d7ba5df9..3ca0181debd9c169aa6ab7dc0697af82f5ce2885 100644
GIT binary patch
delta 328
zcmV-O0k{5$1BnA6iBL{Q4GJ0x0000DNk~Le0000q0000W1Oos70oWFH!;v9Oe+NlK
zK~yM_V_*OSR)zuw1`ZYl1_Ur*zyQ2Ju?B_@m=Xw}z`zJ3IpCT(U<`hIy3hfmAHxO^
z%>u-10U%bUA&_{$z;NLK$Z3w#I3yq{fWQHW8#qZZo-hF0*#Ktd3qXV*K4B4u(Ck2b
zU<1foAE53~cmU$TyqONv#m%tce*;$o3seL|Gd|#f*^mITMS!}lrUqbq(SLw}!41Km
zfROV51_?_8g3qG>Rx$toKZXSiXBfB*`2TO{{|%O60f$NlEIfb|+wX%=Z66@SOt=*D
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aj0pfjhcnHcJqcd`0000<MNUMnLSTYy8huRw

delta 327
zcmV-N0l5B&1Be45iBL{Q4GJ0x0000DNk~Le0000o0000W1Oos70o4cwgpnake+EfJ
zK~#90V_*OS2QbOYfD<$@urn|)Jz!uEz^w)b*ku_QIDj-iKbXq_;SmGk8JNH{3lJaJ
z05pN&AdqAP@&tkQ@-R$zz|z11Qw(x*0ujz31t=hx!XJ3RbOM+xILr#Bfh40Fh{1SR
z032Yv5EuI}fLzPK%LV2oFK9@BfBBgWh(E$j1%@IpG#aSuYRZA^ve!VjCBXR-a2E3d
zptm}Zlr8`fTL1q);4<J{!0?&j|8I`>8^AJNK+F-q@ByL@Na?*%fUx<&m~8@FhP&<{
z1LOP|pg0AF>AQ(gv$rt(|HA$M10TaC28Lo32Wmqojvo^kSR7E@-UOl69c^GJAko)!
Z1^~YGFi}%htDyh@002ovPDHLkV1kRAfGPk0

diff --git a/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img68.png b/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img68.png
index 7304bf3a5a586e326783e595260be6328aee2c90..8db096591f2d765ed209ca94d7ca7c0d461bf91c 100644
GIT binary patch
delta 208
zcmX@dc$ZPJGr-TCmrII^fq{Y7)59eQNb>-(91Al81LIt$OP3}piq}_EROIC3BqSt+
zgoJo_c-Yw3sHmt&NJ#MTfYff=ZPy8;7)yfuf*Bm1-ADs+;yhg(LpWw8CnP*bc#zD%
z$jGMgz>-1fzHLL%O-YFv5(}~>9Bq7XfJtHEfd=s$hFM|^A<3*M#Y`LLGliwTzqj{r
zD%0a#k_xtSd1flyQ)52nu5jx6HI|O#jneJRdzhIS%0k4aw6=d;544KG)78&qol`;+
E0OK}7EdT%j

delta 193
zcmcc1c#cuAGr-TCmrII^fq{Y7)59eQNOJ?REDJLO1LIGw-K-N8#p`o&auN~}LPA13
zJUnb{YzzzxR8&+XBqVrvcz|j@_D!+|Qj8@*e!&b5&u*jvIsTq5jv*Cuk`odhBsMhg
z^6&|;DKlFoBquyLEWpCl&cMdzmm|b+U<KP2#uaVsDZJVO*B^%WvqsqFGfjHKnZwJY
oQ2s%y!KZ37lTu};xX5G%hCS>%V!S@z0GiF<>FVdQ&MBb@00b~KK>z>%

diff --git a/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img69.png b/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img69.png
index c6da046cf7a9ec72eb3500801e3a683c02de82d3..c69666acc88d7163c549850b619488e9fb59f314 100644
GIT binary patch
delta 223
zcmV<503iRG0-*vSiBL{Q4GJ0x0000DNk~Le0000a0000E1Oos70m2@WZIK~Nf1gQ2
zK~xx(V_*OQ2QbMG#0m^73=GT+Oa%-u@PI)MB*G3>@tXk^NGmWfa4;J%FfcM);pAt)
z2@U~qz5tM51}S0@2NI0j3VoblNdtxtER0~50K*mL!?;ah;Anu*j4%2RK!sd>LKz+m
zP)QaB{|O8nzZf(a7BHM)fclU1H8+Dp1jACeNh}}-ZD6>-azFtlbpAgO{9)+7epdj@
Z2LRtN9}2<3lx+Y2002ovPDHLkV1jjwM$iBN

delta 216
zcmV;}04M*U0-6FLiBL{Q4GJ0x0000DNk~Le0000Y0000E1Oos70nY&ADv=>ff0#)`
zK~#90V_*P*00tP?0Ae%paxoyl2L{FsFF_1O5HSHJ%)tvJ*d2jH1H%PYCI(!9;{uQn
z{s7Xy0Z0@a2I=5sQD^|m3h*)<_yAVMz;NN?G@Pa|eS<P&m%WBCH2f1F4CV#=5G4&P
zKt=r%m>ReYco%?`Ffha?uy8bRE+@cD0b0uTje%dl2j*V+{~*x7@we_Gm=6F-tRp@p
SBn5Z?0000<MNUMnLSTZ>rAhGs

diff --git a/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img7.png b/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img7.png
index 66c1a760ddbed53ef656749d321dbf4a96344fcc..72c7d4979e7f995a94a6ce2758182835059c0e6c 100644
GIT binary patch
literal 159
zcmeAS@N?(olHy`uVBq!ia0vp^JV4CH!py+HIB&`YPasD+z$e6Y^XAQS=FDknX{o5F
z2nh+Xv9U2QFyP?<DSr5kuM|izmIV0)GdMiEkp|=#dAc};aLi0jXlP{8ILqj4AUB7X
z>7+v{FV6}IHVNgZ15r{ejVi(J?aVF58x}M)0S)rv;t1<aTr(4>o59o7&t;ucLK6Ua
C>nkz<

literal 163
zcmeAS@N?(olHy`uVBq!ia0vp^AT}QhGXn$T<gNvLK#p{PPl)U0&70@UnKNO+gqD_;
zkdP1?8yg7;2_7CEpuBkEYD*x+SQ6wH%;50sMjDV~=IP=XQZXkvfuWg=Z5tCCpFsCS
zMn0(p5^T379=Y%&<hE=>3j1OP=4MxSZjU9+jDAriCI$=)t-_oOc&aup0-C_!>FVdQ
I&MBb@0LU0C`v3p{

diff --git a/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img70.png b/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img70.png
index e2c9ebb33ca65830751d18c6c7fbf4b1e532c7e2..9e0d0b001bab206c4c43a39168a1d1ba08c02d38 100644
GIT binary patch
delta 319
zcmV-F0l@zH0)PV{iBL{Q4GJ0x0000DNk~Le0000h0000W1Oos70S>dQrja2`fBs2C
zK~yM_V_*P*4j^_YV1R-DAc6(XW#9l29~f|h02qUvfq_wg1Il6K!J`EZG&mF(7#=_@
z*}$;j1A_uY+=ho?1Haoxm^;`&ga9!H;s;DHa~|mdtpfrF5TB7DfCJ)u1_NdW20jJ|
zKEMNU7eCN53QPe8jE#N_+z@jbe;7EJ4VWNokP!?MD0dsVfN|cxiNFX;fbk_E)C!>E
z7ch7*Ft8qg2pj^FAHaAs1IPdW4qyRqFqr{VodA-wfttb(BA7S|7%Esm!kd}pI{q*~
z!i9n1{s)HtUm02%80Jr8X#fRLIg)$8LBz$tbAW-R0ok2FFh(Oq-laAG6#!R7DrgLh
RhMNEY002ovPDHLkV1igjZaM$}

delta 313
zcmV-90mlA-1Ns6XiBL{Q4GJ0x0000DNk~Le0000f0000W1Oos70SZQZn~@<*fA~p6
zK~#90tx~-X0YMP{cKzHBXO-7TE}no^<0MMOzJXIqL?Tfs?hVvBi5Kt)9)VUPS{2c0
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z7_^@q$L!*d)jog=Sb)?MX&Qy3e^Pm-M+^s^f~2rY?Sy)?L{Trxxb&H8hJ)2fb#Oxb
zs_1+8hZ8-~^tlyAj7wsMuqp06(k{D703NV`d2%(`{F0nJ0t<eg+%~OoCae1>Mj>TO
zy15^%DYGH-5~xI%Lb$hTi+R@Tdq^f>g+0)H(`N^1VEu3ApKu4?lO@!;51ov@00000
LNkvXXu0mjfdX0oC

diff --git a/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img71.png b/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img71.png
index debbaf27866d46a2ddfb446540cfa5d64f27ee91..a2fb06cfa206ba9a9608d4f1ad9c9f03df2b2b06 100644
GIT binary patch
literal 245
zcmeAS@N?(olHy`uVBq!ia0vp^GC<77!py+HxYH_dA&{dL;1lAydGqEKD^|>zGiSnt
z2`w!x6%`dZIXNLAAs!wc1_lNyDk>5Z5<EOSK;^=R<jjE-V@Z%-FoVOh8)-mJrKgKy
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zCvdspA=3;ohF6b|F6wP;+{@7Vx`=t^@k0-8A9zqb{i)s&FLt(Tvw3*RB`fqDR3s&e
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literal 227
zcmeAS@N?(olHy`uVBq!ia0vp^Qb5ed!py+HxJ5<r8IYqA;1lAydGqEKD^|>zGpD7c
zrJ|xDCnqN)B*eqR!@$5mLPCOvhX<%|W#obLK#H*>$S;_|;n|HeASc(;#WAE}PI7_+
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VXuP&;*?pkJ44$rjF6*2UngC39OVt1X

diff --git a/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img72.png b/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img72.png
index 5ec63289314d1c60da132bf754e8c024ee4adb65..784daab071cc98fc0a6ac386d577e34391291cf9 100644
GIT binary patch
delta 474
zcmV<00VV#D1eydPiBL{Q4GJ0x0000DNk~Le0001N0000Z1Oos70rWw_(UBocf0#)`
zK~y-6?NqT!13?gdx$K#QOYYWEM7R%#g+CCkl88lum0*)f1RFao&q7IO3bEBs2v}Me
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zWpn_MpiMayv(A{p4GndgC#SMXe^}}xIHIib7Kb$ZeV|lWDDt96<lWK|5A$N3h7;Dr
zLf|Ulq0cH`N;-CO0fZ1#l73GyrIheSEe^X_f&M90?|hnlt+UBihq{Qcqlv_Y4OLI(
zKr})kUsQpR8}+QP#AcUTH4fFJ_ZQ4W$ao0ko)FT|3{6g4TdhKjE5oi5e@*-pq($Y5
z&$NtXZ^v1CGnaC;#8a-k#2g&8+n4k9_foiXnB3;kJ67LPEK>g~<^%0W&htli*5V>H
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Q;s5{u07*qoM6N<$f-ObaAOHXW

delta 466
zcmV;@0WJQT1d;?HiBL{Q4GJ0x0000DNk~Le0001M0000Z1Oos70T!LvsF5K|e~?K;
zK~#90?NqT&!!QtiNuywzHtx`grD5V17$XM6M)`vb>}6m^>A>Cvi7{-9`~b9{kOip=
zYT*YOi3JHHbB>*arcr|sf~9XbU*5etU(S{R4NI@w0iUA|0fZFw*Q<6yn0D%2F7ak<
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diff --git a/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img73.png b/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img73.png
index 51b2f9732fee48743ea368ab5d1845aa918776ad..1b231e7c8a0a85588b402b8f2d8b3afb4f748f3c 100644
GIT binary patch
delta 386
zcmV-|0e$|w1H%I$iBL{Q4GJ0x0000DNk~Le0000@0000W1Oos70n$p?k&z)xe?dt^
zK~y-6-BUYK!!QtiiWO{zfLzj%Be<p#GZYz`WH>=Cz$8a-L!X|40uCVH0(=e--vCol
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zaJZA!j*!_S#DP*!33WBShqh^B$ZD`FAfo2FT;P#N8N<HRI<)6WRu=44*Oh)qv7O*!
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zWP;E>-r%`4w7<a<MZ6;lN?2iy)Akl;mKV*xB`$%vP5<EHcd|e{t(_xZ`x{St(A*Wm
gd94%MDt~({0ajd9PlzTL)Bpeg07*qoM6N<$g7?&^&;S4c

delta 379
zcmV->0fhd;1H1zviBL{Q4GJ0x0000DNk~Le0000>0000W1Oos70pC=p){!Ahe>zD-
zK~#90<x{&(!!Q&*N!%#3O`H*lfsU0}_=L<X<qwF&jw&HB`vY1e{(w)&AJBoFF6>OK
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Z@C|c&Nb^A>9P$7F002ovPDHLkV1hGFu)hER

diff --git a/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img74.png b/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img74.png
index 4588b8ba5b04cb33441b24c80806e4c11cc45df8..933552a581c8ee743b0f593849edfc7bd7c44fc7 100644
GIT binary patch
delta 386
zcmV-|0e$|o1H%I$iBL{Q4GJ0x0000DNk~Le0000z0000W1Oos70VD%m36UX8e?dt^
zK~yM_)ly4J#6S>zJ?UgRWM(?J5kW9V$PogH2!fL%c!Qap+swwTa{~1S22U`!7CeIE
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gtNiTSiTodY0BF!e+Wr+C_5c6?07*qoM6N<$g6j&bRR910

delta 371
zcmV-(0gV2`1GEDniBL{Q4GJ0x0000DNk~Le0000y0000W1Oos70n5QQH<2Mse=<o#
zK~#90%~HKe!%!6d5<{*g!~`5g>KJe^5217N2IdL0Z{XFbi{K+%7s1I4ZVm>-*^G_>
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diff --git a/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img75.png b/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img75.png
index bf6a805805f17211c1d45efb53c716ad3c418f8f..040bda610c0b03039e5bd5ccd51933369f3c5e9b 100644
GIT binary patch
delta 201
zcmaFN_=HilGr-TCmrII^fq{Y7)59eQNDBfn9}6=B1EbH8TOf|^L{-&#6%`c;2?-t^
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delta 200
zcmaFD_?S_(Gr-TCmrII^fq{Y7)59eQNb>_R9}6=B17qppY%d_kV4|vOy@7#&ii(Pa
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diff --git a/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img76.png b/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img76.png
index 72bf0c871ade33ff8434fb73dfa61939a32f9426..ae00dc154a2dce1cc5a7bf698a6ccc386c616051 100644
GIT binary patch
delta 1089
zcmV-H1it(82>b{kiBL{Q4GJ0x0000DNk~Le0003i0000c1Oos70U2bFdyyebfBH#8
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Hu0mjfoMar4

delta 1080
zcmV-81jqaQ2=fRbiBL{Q4GJ0x0000DNk~Le0003h0000b1Oos70dO*j>yaT$fAL8~
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diff --git a/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img77.png b/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img77.png
index f8c2551faf6f5400dead0aa9d8b88206f247fb12..53c2a77bceaebc2495afc7487900a9afe63ee478 100644
GIT binary patch
delta 492
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delta 494
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diff --git a/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img78.png b/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img78.png
index 5beca6ec03b04041fa73f785aaf975b99abf9975..cadb86bf8c4896e2ffe635f7b150ab11caea3f4f 100644
GIT binary patch
delta 785
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delta 802
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diff --git a/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img79.png b/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img79.png
index 5c8a7735cc70c49a84dc75f1aa46345959048782..18a99a6aa12d5e8d4f0295853fe81997a605a9a0 100644
GIT binary patch
delta 200
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delta 198
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diff --git a/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img8.png b/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img8.png
index 25aa0a7e32db3a4eabc4c80b4926b7a1988ee532..09bf5c41145a2541ac84b4b683be452bd239d51e 100644
GIT binary patch
delta 446
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delta 442
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diff --git a/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img80.png b/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img80.png
index 1a69c9a2fef1c5bf99353fd6d1d2d0146ae89635..4a5f786f1599a2ff95ddbff8c7ed094bbee59de9 100644
GIT binary patch
delta 1258
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delta 1256
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diff --git a/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img81.png b/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img81.png
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diff --git a/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img82.png b/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img82.png
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GIT binary patch
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diff --git a/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img83.png b/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img83.png
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diff --git a/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img84.png b/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img84.png
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diff --git a/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img85.png b/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img85.png
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delta 145
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diff --git a/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img87.png b/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img87.png
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diff --git a/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img89.png b/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img89.png
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diff --git a/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img9.png b/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img9.png
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delta 355
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diff --git a/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img90.png b/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img90.png
index d31fa8e7a0b6468ea70f20ea79b65977694cb020..f602f9496bc71951c496d2a2f791445fa6946440 100644
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delta 235
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diff --git a/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img91.png b/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img91.png
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diff --git a/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img92.png b/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img92.png
index 839879187c21bd7a0f6be1f94433f1ff3c730bb2..99aaee1866680d150aa9445acbf7b27ace8a5a36 100644
GIT binary patch
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delta 284
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diff --git a/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img93.png b/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img93.png
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diff --git a/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img94.png b/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img94.png
index 75be22136795762737797118b5ef74a8871c327b..48fbbd7df8f2b181fe67413e8d14b86a32cbffee 100644
GIT binary patch
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delta 421
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diff --git a/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img95.png b/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img95.png
index 2fd953d060f3121393da1b556b1c70bebaae0b98..5614d58f22ed467e05a688eaac57246318d6207b 100644
GIT binary patch
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delta 517
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diff --git a/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img96.png b/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img96.png
index 1cf25a057e277a44ba37e52b08fccafa046462d1..ffc82543e56fcb5a47e821d711e2cd3551a9c872 100644
GIT binary patch
delta 221
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delta 217
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diff --git a/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img97.png b/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img97.png
index 5a0de42877c990b650549cc9b19870444cfe2587..23bf8a4cd4caf342bfc1406558e77e4d6af73117 100644
GIT binary patch
delta 329
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delta 341
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diff --git a/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img98.png b/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img98.png
index f14d302f9d5479f35cafafe1a6fd37ac8b3f4070..074293292dd4d51725eb0aaba07bc7033b3371a6 100644
GIT binary patch
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delta 166
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diff --git a/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img99.png b/deal.II/doc/tutorial/chapter-2.step-by-step/step-18.data/intro/img99.png
index afad9fedacbd956d882322d605b9dd8125ccaedf..60d2b911055fd784c656a9284c7acf15bc62479a 100644
GIT binary patch
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literal 215
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-- 
2.39.5