@endcode
-
-
-
-
-The last solution, as written by the program at the end of the
-<code>%run()</code> function, looks as follows:
-
-
-
-@image html step-6.solution.png
-
-
-
-After each refinement, the solution after the fifth Newton-
-iteration is shown in the following pictures. On the left
-the solution is visualized, on the right side the solution
-with the mesh is shown:
-
+We can visualize the solution after each set of five Newton
+iterations, i.e., on each of the meshes on which we approximate the
+solution. This yields the following set of images:
<TABLE WIDTH="100%">
<tr>
<td>
- @image html step-6.grid-0.png
+ @image html step-15.solution-0.png
</td>
<td>
- @image html step-6.grid-1.png
+ @image html step-15.solution-1.png
</td>
</tr>
<tr>
<td>
- @image html step-6.grid-2.png
+ @image html step-15.solution-2.png
</td>
<td>
- @image html step-6.grid-3.png
+ @image html step-15.solution-3.png
</td>
</tr>
<tr>
<td>
- @image html step-6.grid-4.png
+ @image html step-15.solution-4.png
</td>
<td>
- @image html step-6.grid-5.png
+ @image html step-15.solution-5.png
</td>
</tr>
<tr>
<td>
- @image html step-6.grid-6.png
+ @image html step-15.solution-6.png
</td>
<td>
- @image html step-6.grid-7.png
+ @image html step-15.solution-7.png
</td>
</tr>
</table>
It is clearly visible, that the solution minimizes the surface
-after each refinement. The solution converges to a picture one
-would imagine a soapbubble inside a wire, which is bended like
-the boundary. Also it is visible, how the boundary
+after each refinement. The solution converges to a picture one
+would imagine a soapbubble to be that is located inside a wire loop
+that is bent like
+the boundary. Also it is visible, how the boundary
is smoothed out after each refinement. On the coarse mesh,
the boundary doesn't look like a sine, whereas it does the
finer the mesh gets.
The mesh is mostly refined near the boundary, where the solution
-increases or decreases strongly, whereas it is coarsened on
+increases or decreases strongly, whereas it is coarsened on
the inside of the domain, where nothing interesting happens,
-because there isn't much change in the solution.
+because there isn't much change in the solution. The final solution
+and mesh are shown here:
+@image html step-15.grid.png