]> https://gitweb.dealii.org/ - dealii-svn.git/commitdiff
Fix maths.
authorwolf <wolf@0785d39b-7218-0410-832d-ea1e28bc413d>
Thu, 30 Jan 2003 02:38:50 +0000 (02:38 +0000)
committerwolf <wolf@0785d39b-7218-0410-832d-ea1e28bc413d>
Thu, 30 Jan 2003 02:38:50 +0000 (02:38 +0000)
git-svn-id: https://svn.dealii.org/trunk@6991 0785d39b-7218-0410-832d-ea1e28bc413d

deal.II/doc/tutorial/chapter-2.step-by-step/step-14.data/intro.tex

index accc91cb6ba0f2c8dfc8fd130831bf17a5cdb4ac..4241f550742807c4fc0fa1d12472e970fad5e8f4 100644 (file)
@@ -5,7 +5,7 @@
 \section{The maths}
 
 The Heidelberg group of Professor Rolf Rannacher, to which the three main
-authors of the deal.II library belonged for the PhD time and partly also
+authors of the deal.II library belonged during their PhD time and partly also
 afterwards, has been involved with adaptivity and error estimation for finite
 element discretizations since the mid-90ies. The main achievement is the
 development of error estimates for arbitrary functionals of the solution, and
@@ -92,7 +92,7 @@ Thus, we have
 \begin{align*}
   J(e)
   &=
-  \sum_K (f+u_h), z-\varphi_h)_K
+  \sum_K (f+\Delta u_h, z-\varphi_h)_K
   - (\partial_n u_h, z-\varphi_h)_{\partial K\backslash \partial\Omega}.
 \end{align*}
 In a final step, note that when taking the normal derivative of $u_h$, we mean
@@ -103,7 +103,7 @@ with the neighbor cell $K'$, to obtain
 \begin{align*}
   J(e)
   &=
-  \sum_K (f+u_h), z-\varphi_h)_K
+  \sum_K (f+\Delta u_h, z-\varphi_h)_K
   - \frac 12 (\partial_n u_h|_K + \partial_{n'} u_h|_{K'},
               z-\varphi_h)_{\partial K\backslash \partial\Omega}.  
 \end{align*}
@@ -120,7 +120,7 @@ $\varphi_h=I_h z$:
 \begin{align*}
   J(e)
   &=
-  \sum_K (f+u_h), z-I_h z)_K
+  \sum_K (f+\Delta u_h, z-I_h z)_K
   - \frac 12 ([\partial_n u_h],
               z-I_h z)_{\partial K\backslash \partial\Omega}.  
 \end{align*}

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