]> https://gitweb.dealii.org/ - dealii-svn.git/commitdiff
More doxygenization work
authorwolf <wolf@0785d39b-7218-0410-832d-ea1e28bc413d>
Tue, 28 Mar 2006 06:15:27 +0000 (06:15 +0000)
committerwolf <wolf@0785d39b-7218-0410-832d-ea1e28bc413d>
Tue, 28 Mar 2006 06:15:27 +0000 (06:15 +0000)
git-svn-id: https://svn.dealii.org/trunk@12708 0785d39b-7218-0410-832d-ea1e28bc413d

47 files changed:
deal.II/doc/tutorial/chapter-2.step-by-step/step-10.data/ball_mapping_q1_ref0.jpg [deleted file]
deal.II/doc/tutorial/chapter-2.step-by-step/step-10.data/ball_mapping_q1_ref1.jpg [deleted file]
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deal.II/doc/tutorial/chapter-2.step-by-step/step-10.data/quarter-q1.jpg [deleted file]
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deal.II/doc/tutorial/chapter-2.step-by-step/step-10.data/results.dox [moved from deal.II/doc/tutorial/chapter-2.step-by-step/step-10.data/results.html with 78% similarity]
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deal.II/doc/tutorial/chapter-2.step-by-step/step-16.data/intro.dox [moved from deal.II/doc/tutorial/chapter-2.step-by-step/step-16.data/intro.html with 81% similarity]
deal.II/doc/tutorial/chapter-2.step-by-step/step-16.data/results.dox [moved from deal.II/doc/tutorial/chapter-2.step-by-step/step-16.data/results.html with 100% similarity]
deal.II/doc/tutorial/chapter-2.step-by-step/step-8.data/displacement-vectors.jpg [deleted file]
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deal.II/doc/tutorial/chapter-2.step-by-step/step-8.data/step-8.grid.png [new file with mode: 0644]
deal.II/doc/tutorial/chapter-2.step-by-step/step-8.data/step-8.vectors.png [new file with mode: 0644]
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similarity index 79%
rename from deal.II/doc/tutorial/chapter-2.step-by-step/step-10.data/intro.html
rename to deal.II/doc/tutorial/chapter-2.step-by-step/step-10.data/intro.dox
index 7cc6081ef17e78cdb8b3a27eaa51c4db25e4f0ae..2749945848d5a8226f1e36efaa6aa4b3aef3cc65 100644 (file)
@@ -1,9 +1,9 @@
 <a name="Intro"></a>
 <h1>Introduction</h1>
 
-<p>
+
 This is a rather short example which only shows some aspects of using
-higher order mappings. By <it>mapping</it> we mean the transformation
+higher order mappings. By <em>mapping</em> we mean the transformation
 between the unit cell (i.e. the unit line, square, or cube) to the
 cells in real space. In all the previous examples, we have implicitly
 used linear or d-linear mappings; you will not have noticed this at
@@ -14,16 +14,16 @@ cases where the piecewise linear approximation of the boundary
 your computational domain is an approximation to the real domain using
 curved boundaries as well. If the boundary approximation uses
 piecewise quadratic parabolas to approximate the true boundary, then
-we say that this is a quadratic or <em>Q<sub>2</sub></em> approximation. If we
-use piecewise graphs of cubic polynomials, then this is a <em>Q<sub>3</sub></em>
+we say that this is a quadratic or $Q_2$ approximation. If we
+use piecewise graphs of cubic polynomials, then this is a $Q_3$
 approximation, and so on.
-</p>
 
-<p>
+
+
 For some differential equations, it is known that piecewise linear
-approximations of the boundary, i.e. Q<sub>1</sub> mappings, are not
+approximations of the boundary, i.e. $Q_1$ mappings, are not
 sufficient if the boundary of the domain is curved. Examples are the
-biharmonic equation using C<sup>1</sup> elements, or the Euler
+biharmonic equation using $C^1$ elements, or the Euler
 equation on domains with curved reflective boundaries. In these cases,
 it is necessary to compute the integrals using a higher order
 mapping. The reason, of course, is that if we do not use a higher
@@ -31,31 +31,31 @@ order mapping, the order of approximation of the boundary dominates
 the order of convergence of the entire numerical scheme, irrespective
 of the order of convergence of the discretization in the interior of
 the domain.
-</p>
 
-<p>
+
+
 Rather than demonstrating the use of higher order mappings with one of
 these more complicated examples, we do only a brief computation:
-calculating the value of pi=3.141592653589793238462643... by two
+calculating the value of $\pi=3.141592653589793238462643\ldots$ by two
 different methods.
-</p>
 
-<p>
+
+
 The first method uses a triangulated approximation of the circle with
 unit radius and integrates the unit function over it. Of course, if
 the domain were the exact unit circle, then the area would be pi, but
 since we only use an approximation by piecewise polynomial segments,
 the value of the area is not exactly pi. However, it is known that as
-we refine the triangulation, a Q<sub>p</sub> mapping approximates the boundary
-with an order <it>h<sup>p+1</sup></it>, where <it>h</it> is the mesh
+we refine the triangulation, a $Q_p$ mapping approximates the boundary
+with an order $h^{p+1}$, where $h$ is the mesh
 width. We will check the values of the computed area of the circle and
 their convergence towards pi under mesh refinement for different
 mappings. We will also find a convergence behavior that is surprising
 at first, but has a good explanation.
-</p>
 
-<p>
+
+
 The second method works similarly, but this time does not use the area
 of the triangulated unit circle, but rather its perimeter. Pi is then
 approximated by half of the perimeter, as the radius is equal to one.
-</p>
+
diff --git a/deal.II/doc/tutorial/chapter-2.step-by-step/step-10.data/quarter-q1.jpg b/deal.II/doc/tutorial/chapter-2.step-by-step/step-10.data/quarter-q1.jpg
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similarity index 78%
rename from deal.II/doc/tutorial/chapter-2.step-by-step/step-10.data/results.html
rename to deal.II/doc/tutorial/chapter-2.step-by-step/step-10.data/results.dox
index 4fc34ce541793897b3ec2bb8cff356b18fe9be8e..cccf2683e589a3e18ecb2fb9deed20e262c62e6d 100644 (file)
@@ -1,27 +1,27 @@
 <a name="Results"></a>
 <h1>Results</h1>
 
-<p>
+
 The program performs two tasks, the first being to generate a
 visualization of the mapped domain, the second to compute pi by the
 two methods described. Let us first take a look at the generated
 graphics. They are generated in Gnuplot format, and can be viewed with
 the commands
-<pre>
+@code
 set data style lines
 set size 0.721, 1
 set nokey
 plot [-1:1][-1:1] "ball0_mapping_q1.dat"
-</pre>
+@endcode
 or using one of the other filenames. The second line makes sure that
 the aspect ratio of the generated output is actually 1:1, i.e. a
 circle is drawn as a circle on your screen, rather than as an
 ellipse. The third line switches off the key in the graphic, as that
 will only print information (the filename) which is not that important
 right now.
-</p>
 
-<p>
+
+
 The following table shows the triangulated computational domain for
 Q1, Q2, and Q3 mappings, for the original coarse grid (left), and a
 once uniformly refined grid (right). If your browser does not display
@@ -29,28 +29,28 @@ these pictures in acceptable quality, view them one by one.
 <table "width=80%" align="center">
   <tr>
     <td>
-      <img src="step-10.data/ball_mapping_q1_ref0.jpg" alt="Q1 mapping, coarse grid" height="300">
+      @image html step-10.ball_mapping_q1_ref0.png
     </td>
     <td>
-      <img src="step-10.data/ball_mapping_q1_ref1.jpg" alt="Q1 mapping, once refined grid" height="300">
+      @image html step-10.ball_mapping_q1_ref1.png
     </td>
   </tr>
 
   <tr>
     <td>
-      <img src="step-10.data/ball_mapping_q2_ref0.jpg" alt="Q2 mapping, coarse grid" height="300">
+      @image html step-10.ball_mapping_q2_ref0.png
     </td>
     <td>
-      <img src="step-10.data/ball_mapping_q2_ref1.jpg" alt="Q2 mapping, once refined grid" height="300">
+      @image html step-10.ball_mapping_q2_ref1.png
     </td>
   </tr>
 
   <tr>
     <td>
-      <img src="step-10.data/ball_mapping_q3_ref0.jpg" alt="Q3 mapping, coarse grid" height="300">
+      @image html step-10.ball_mapping_q3_ref0.png
     </td>
     <td>
-      <img src="step-10.data/ball_mapping_q3_ref1.jpg" alt="Q3 mapping, once refined grid" height="300">
+      @image html step-10.ball_mapping_q3_ref1.png
     </td>
   </tr>
 </table>
@@ -62,13 +62,13 @@ with dashed lines the exact circle:
 <table "width=80%" align="center">
   <tr>
     <td>
-      <img src="step-10.data/quarter-q1.jpg" alt="Q1 mapping, coarse grid" height="300">
+      @image html step-10.quarter-q1.png
     </td>
     <td>
-      <img src="step-10.data/quarter-q2.jpg" alt="Q2 mapping, coarse grid" height="300">
+      @image html step-10.quarter-q2.png
     </td>
     <td>
-      <img src="step-10.data/quarter-q3.jpg" alt="Q3 mapping, coarse grid" height="300">
+      @image html step-10.quarter-q3.png
     </td>
   </tr>
 </table>
@@ -82,12 +82,12 @@ only on cells at the boundary. Higher order mappings are therefore
 usually not noticably slower than lower order ones, because the
 additional computations are only performed on a small subset of all
 cells.
-</p>
 
-<p>
+
+
 The second purpose of the program was to compute the value of pi to
 good accuracy. This is the output of this part of the program:
-<pre>
+@code
 Computation of Pi by the area:
 ==============================
 Degree = 1
@@ -164,31 +164,31 @@ cells         eval.pi         error
 320     3.1415926540544636      4.6467e-10      6.00
 1280    3.1415926535970535      7.2602e-12      6.00
 5120    3.1415926535899010      1.0805e-13      6.07
-</pre>
-</p>
+@endcode
+
+
 
-<p>
 One of the immediate observations from the output is that in all cases
 the values converge quickly to the true value of
-pi=3.141592653589793238462643. Note that for the Q<sub>4</sub> mapping, the last
+$\pi=3.141592653589793238462643$. Note that for the $Q_4$ mapping, the last
 number is correct to 13 digits in both computations, which is already
-quite a lot. However, also note that for the Q<sub>1</sub> mapping, even on the
+quite a lot. However, also note that for the $Q_1$ mapping, even on the
 finest grid the accuracy is significantly worse than on the coarse
-grid for a Q<sub>4</sub> mapping!
-</p>
+grid for a $Q_4$ mapping!
+
+
 
-<p>
 The last column of the output shows the convergence order, in powers
-of the mesh width <it>h</it>. In the introduction, we had stated that
-the convergence order for a <it>Q<sub>p</sub></it> mapping should be
-<it>h<sup>p+1</sup></it>. However, in the example shown, the Q<sub>2</sub> and Q<sub>4</sub>
-mappings show a convergence order of <it>h<sup>p+2</sup></it>! This at
+of the mesh width $h$. In the introduction, we had stated that
+the convergence order for a $Q_p$ mapping should be
+$h^{p+1}$. However, in the example shown, the $Q_2$ and $Q_4$
+mappings show a convergence order of $h^{p+2}$! This at
 first surprising fact is readily explained by the particular boundary
 we have chosen in this example. In fact, the circle is described by the function
-<it>sqrt(1-x<sup>2</sup>)</it>, which has the series expansion 
-<it>1-x<sup>2</sup>/2-x<sup>4</sup>/8-x<sup>6</sup>/16+...</it>
-around <it>x=0</it>. Thus, for the quadratic mapping where the
+$\sqrt{1-x^2}$, which has the series expansion 
+$1-x^2/2-x^4/8-x^6/16+\ldots$
+around $x=0$. Thus, for the quadratic mapping where the
 truncation error of the quadratic approximation should be cubic, there
 is no such term but only a quartic one, which raises the convergence
-order to 4, instead of 3. The same happens for the Q<sub>4</sub> mapping.
-</p>
+order to 4, instead of 3. The same happens for the $Q_4$ mapping.
+
diff --git a/deal.II/doc/tutorial/chapter-2.step-by-step/step-10.data/step-10.ball_mapping_q1_ref0.png b/deal.II/doc/tutorial/chapter-2.step-by-step/step-10.data/step-10.ball_mapping_q1_ref0.png
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diff --git a/deal.II/doc/tutorial/chapter-2.step-by-step/step-12.data/grid-5.gif b/deal.II/doc/tutorial/chapter-2.step-by-step/step-12.data/grid-5.gif
deleted file mode 100644 (file)
index 82dedab..0000000
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similarity index 60%
rename from deal.II/doc/tutorial/chapter-2.step-by-step/step-12.data/results.html
rename to deal.II/doc/tutorial/chapter-2.step-by-step/step-12.data/results.dox
index 77e28becba9029e07c67e7c5c4cdb549ef7ff8cf..65b91e31819578c5959d7f98addfe163fb5071ce 100644 (file)
@@ -1,19 +1,18 @@
 <a name="Results"></a>
 <h1>Results</h1>
 
-<p>
+
 The output of this program consist of the console output, the eps
 files including the grids, and the solutions given in gnuplot format.
-<code>
-<pre>
+@code
 Cycle 0:
    Number of active cells:       64
    Number of degrees of freedom: 256
 Time of assemble_system1: 0.05
 Time of assemble_system2: 0.04
 solution1 and solution2 coincide.
-Writing grid to &lt;grid-0.eps&gt;...
-Writing solution to &lt;sol-0.gnuplot&gt;...
+Writing grid to <grid-0.eps>...
+Writing solution to <sol-0.gnuplot>...
 
 Cycle 1:
    Number of active cells:       112
@@ -21,8 +20,8 @@ Cycle 1:
 Time of assemble_system1: 0.09
 Time of assemble_system2: 0.07
 solution1 and solution2 coincide.
-Writing grid to &lt;grid-1.eps&gt;...
-Writing solution to &lt;sol-1.gnuplot&gt;...
+Writing grid to <grid-1.eps>...
+Writing solution to <sol-1.gnuplot>...
 
 Cycle 2:
    Number of active cells:       214
@@ -30,8 +29,8 @@ Cycle 2:
 Time of assemble_system1: 0.17
 Time of assemble_system2: 0.14
 solution1 and solution2 coincide.
-Writing grid to &lt;grid-2.eps&gt;...
-Writing solution to &lt;sol-2.gnuplot&gt;...
+Writing grid to <grid-2.eps>...
+Writing solution to <sol-2.gnuplot>...
 
 Cycle 3:
    Number of active cells:       415
@@ -39,8 +38,8 @@ Cycle 3:
 Time of assemble_system1: 0.32
 Time of assemble_system2: 0.28
 solution1 and solution2 coincide.
-Writing grid to &lt;grid-3.eps&gt;...
-Writing solution to &lt;sol-3.gnuplot&gt;...
+Writing grid to <grid-3.eps>...
+Writing solution to <sol-3.gnuplot>...
 
 Cycle 4:
    Number of active cells:       796
@@ -48,8 +47,8 @@ Cycle 4:
 Time of assemble_system1: 0.62
 Time of assemble_system2: 0.52
 solution1 and solution2 coincide.
-Writing grid to &lt;grid-4.eps&gt;...
-Writing solution to &lt;sol-4.gnuplot&gt;...
+Writing grid to <grid-4.eps>...
+Writing solution to <sol-4.gnuplot>...
 
 Cycle 5:
    Number of active cells:       1561
@@ -57,35 +56,34 @@ Cycle 5:
 Time of assemble_system1: 1.23
 Time of assemble_system2: 1.03
 solution1 and solution2 coincide.
-Writing grid to &lt;grid-5.eps&gt;...
-Writing solution to &lt;sol-5.gnuplot&gt;...
+Writing grid to <grid-5.eps>...
+Writing solution to <sol-5.gnuplot>...
+@endcode
 
-</pre>
-</code>
 We see that, as expected, on each refinement step the two solutions
 coincide. The difference measured in time of treating each face only
 once (second version of the DG method) in comparison with treating
 each face twice within a nested loop over all cells and all faces of
 each cell (first version), is much less than one might have
 expected. The gain is less than 20% on the last few refinement steps.
-</p>
 
-<p> First we show the solutions on the initial mesh, the mesh after two
+
+ First we show the solutions on the initial mesh, the mesh after two
 and after five adaptive refinement steps.
-<p align="center">
-  <img src="step-12.data/sol-0.gif" alt="sol-0.gnuplot" width="75%">
-  <img src="step-12.data/sol-2.gif" alt="sol-2.gnuplot" width="75%">
-  <img src="step-12.data/sol-5.gif" alt="sol-5.gnuplot" width="75%">
-</p>
 
-<p> Then we show the final grid (after 5 refinement steps). The
+@image step-12.sol-0.png
+@image step-12.sol-2.png
+@image step-12.sol-5.png
+
+
+Then we show the final grid (after 5 refinement steps). The
 grid is largely concentrated in the vicinity of the jump of the
 solution.
-<p align="center">
-  <img src="step-12.data/grid-5.gif" alt="grid-5.eps" width="50%">
-</p>
-
-<p> And finally we show a plot of a 3d computation.
-<p align="center">
-  <img src="step-12.data/sol-5-3d.gif" alt="sol-5-3d.eps" width="50%">
-</p>
+
+@image step-12.grid-5.png
+
+
+And finally we show a plot of a 3d computation.
+
+@image html step-12.sol-5-3d.png
+
diff --git a/deal.II/doc/tutorial/chapter-2.step-by-step/step-12.data/sol-0.gif b/deal.II/doc/tutorial/chapter-2.step-by-step/step-12.data/sol-0.gif
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new file mode 100644 (file)
index 0000000..d9cfd87
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similarity index 81%
rename from deal.II/doc/tutorial/chapter-2.step-by-step/step-16.data/intro.html
rename to deal.II/doc/tutorial/chapter-2.step-by-step/step-16.data/intro.dox
index 2d78fbf79150875629922cb5a8c574c4e54e0c68..750048aaefd2aacaf6808cf2aba21f84d68cdd15 100644 (file)
@@ -1,15 +1,15 @@
 <a name="Intro"></a>
 <h1>Introduction</h1>
 
-<p>
+
 This example shows the basic usage of the multilevel functions in
-<tt>deal.II</tt>. It solves the Helmholtz equation with Neumann boundary conditions
+deal.II. It solves the Helmholtz equation with Neumann boundary conditions
 to avoid additional complications due to Dirichlet boundary conditions (there,
 some library functions are missing). Therefore, the solution is the constant
 function with value unity. In all other respects, it is similar to step 5.
-</p>
 
-<p> In order to allow sufficient flexibility in conjunction with systems of
+
+ In order to allow sufficient flexibility in conjunction with systems of
 differential equations and block preconditioners, quite a few different objects
 have to be created before starting the multilevel method. These are
 <ul>
@@ -19,17 +19,17 @@ have to be created before starting the multilevel method. These are
 <li>MGMatrix, the matrix object having a special level multiplication, i.e. we
 basically store one matrix per grid level and allow multiplication with it.
 </ul>
-</p>
 
-<p>
+
+
 These objects are combined in an object of type Multigrid, containing the
 implementation of the V-cycle, which is in turn used by the preconditioner
 PreconditionMG, ready for plug-in into a linear solver of the LAC library.
-</p>
 
-<p>
-The multilevel method in <tt>deal.II</tt> follows in many respects the outlines
+
+
+The multilevel method in deal.II follows in many respects the outlines
 of the various publications by James Bramble, Joseph Pasciak and Jinchao Xu. In
 order to understand many of the options, a rough familiarity with their work is
 quite helpful.
-</p>
+
diff --git a/deal.II/doc/tutorial/chapter-2.step-by-step/step-8.data/displacement-vectors.jpg b/deal.II/doc/tutorial/chapter-2.step-by-step/step-8.data/displacement-vectors.jpg
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similarity index 70%
rename from deal.II/doc/tutorial/chapter-2.step-by-step/step-8.data/results.html
rename to deal.II/doc/tutorial/chapter-2.step-by-step/step-8.data/results.dox
index 9f7c98cdf3c9a61ef6c4f80b1d6147fdfb8cef93..bc6a11423ea34e5c21767ad61e093659cd657737 100644 (file)
@@ -1,50 +1,47 @@
 <a name="Results"></a>
 <h1>Results</h1>
 
-<p>
+
 There is not much to be said about the results of this program, apart
 from that they look nice. All images were made using GMV from the
 output files that the program wrote to disk. The first picture shows
 the displacement as a vector field, where one vector is shown at each
 vertex of the grid:
-</p>
 
-<p ALIGN=CENTER>
-<IMG SRC="step-8.data/displacement-vectors.jpg" ALT="displacement-vectors" WIDTH="300">
-</p>
 
-<p>
+@image html step-8.vectors.png
+
+
 You can clearly see the sources of x-displacement around x=0.5 and
 x=-0.5, and of y-displacement at the origin. The next image shows the
 final grid after eight steps of refinement:
-</p>
 
-<p ALIGN=CENTER>
-<IMG SRC="step-8.data/final-grid.jpg" ALT="final-grid" WIDTH="300">
-</p>
 
-<p>
+@image html step-8.grid.png
+
+
+
 Finally, the x-displacement and y-displacement are displayed separately:
-</p>
 
-<p>
+
+
 <TABLE WIDTH="100%">
 <tr>
 <td>
-<IMG SRC="step-8.data/displacement-x.jpg" ALT="displacement-x" WIDTH="300">
+@image html step-8.x.png
 </td>
 <td>
-<IMG SRC="step-8.data/displacement-y.jpg" ALT="displacement-y" WIDTH="300">
+@image html step-8.y.png
 </td>
 </tr>
 </table>
-</p>
 
-<p>
+
+
 It should be noted that intuitively one would have expected the
 solution to be symmetric about the x- and y-axes since the x- and
 y-forces are symmetric with respect to these axes. However, the force
 considered as a vector is not symmetric and consequently neither is
 the solution.
-</p>
+
 
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similarity index 84%
rename from deal.II/doc/tutorial/chapter-2.step-by-step/step-9.data/results.html
rename to deal.II/doc/tutorial/chapter-2.step-by-step/step-9.data/results.dox
index eace7e86f097644f134d81186e9b56a578cca2c9..0217858a784168b463b48d720034f7bfe33d8500 100644 (file)
@@ -1,12 +1,11 @@
 <a name="Results"></a>
 <h1>Results</h1>
 
-<p>
+
 The results of this program are not particularly spectacular. They
 consist of the console output, some grid files, and the solution on
 the finest grid. First for the console output:
-<code>
-<pre>
+@code
 Cycle 0:
    Number of active cells:       256
    Number of degrees of freedom: 289
@@ -25,31 +24,27 @@ Cycle 4:
 Cycle 5:
    Number of active cells:       26002
    Number of degrees of freedom: 30035
-</pre>
-</code>
+@endcode
 As can be seen, quite a number of cells is used on the finest level to
 resolve the features of the solution. The final grid showing this is
 displayed in the following picture:
-</p>
 
-<p align="center">
-  <img src="step-9.data/final-grid.gif" alt="final grid" width="50%">
-</p>
 
-<p>
+@image html step-9.grid.png
+
+
+
 The structure of the grid will be understandable by looking at the
 solution itself:
-</p>
 
-<p align="center">
-  <img src="step-9.data/final-solution.jpeg" alt="final solution" width="50%">
-</p>
 
-<p>
+@image html step-9.solution.png
+
+
+
 Note that the solution is created by that part that is transported
 along the wiggled advection field from the left and lower boundaries
 to the top right, and the part that is created by the source in the
 lower left corner, and the results of which are also transported
 along. The grid shown above is well-adapted to resolve these
 features. 
-</p>
\ No newline at end of file
diff --git a/deal.II/doc/tutorial/chapter-2.step-by-step/step-9.data/step-9.grid.png b/deal.II/doc/tutorial/chapter-2.step-by-step/step-9.data/step-9.grid.png
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diff --git a/deal.II/doc/tutorial/chapter-2.step-by-step/step-9.data/step-9.solution.png b/deal.II/doc/tutorial/chapter-2.step-by-step/step-9.data/step-9.solution.png
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index 0000000..e5164f3
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