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>
- <img src="https://www.dealii.org/images/steps/developer/step-15.solution-0.png" alt="">
-</td>
-<td>
- <img src="https://www.dealii.org/images/steps/developer/step-15.solution-1.png" alt="">
-</td>
-</tr>
-
-<tr>
-<td>
- <img src="https://www.dealii.org/images/steps/developer/step-15.solution-2.png" alt="">
-</td>
-<td>
- <img src="https://www.dealii.org/images/steps/developer/step-15.solution-3.png" alt="">
-</td>
-</tr>
-
-<tr>
-<td>
- <img src="https://www.dealii.org/images/steps/developer/step-15.solution-4.png" alt="">
-</td>
-<td>
- <img src="https://www.dealii.org/images/steps/developer/step-15.solution-5.png" alt="">
-</td>
-</tr>
-
-<tr>
-<td>
- <img src="https://www.dealii.org/images/steps/developer/step-15.solution-6.png" alt="">
-</td>
-<td>
- <img src="https://www.dealii.org/images/steps/developer/step-15.solution-7.png" alt="">
-</td>
-</tr>
-</table>
+<div class="twocolumn" style="width: 80%">
+ <div>
+ <img src="https://www.dealii.org/images/steps/developer/step_15_solution_1.png"
+ alt="Solution after zero cycles with countour lines." width="230" height="273">
+ </div>
+ <div>
+ <img src="https://www.dealii.org/images/steps/developer/step_15_solution_2.png"
+ alt="Solution after one cycle with countour lines." width="230" height="273">
+ </div>
+ <div>
+ <img src="https://www.dealii.org/images/steps/developer/step_15_solution_3.png"
+ alt="Solution after two cycles with countour lines." width="230" height="273">
+ </div>
+ <div>
+ <img src="https://www.dealii.org/images/steps/developer/step_15_solution_4.png"
+ alt="Solution after three cycles with countour lines." width="230" height="273">
+ </div>
+</div>
It is clearly visible, that the solution minimizes the surface
after each refinement. The solution converges to a picture one
The mesh is mostly refined near the boundary, where the solution
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. The final solution
-and mesh are shown here:
-
-<img src="https://www.dealii.org/images/steps/developer/step-15.grid.png" alt="">
+because there isn't much change in the solution. The ninth
+solution and mesh are shown here:
+
+<div class="onecolumn" style="width: 60%">
+ <div>
+ <img src="https://www.dealii.org/images/steps/developer/step_15_solution_9.png"
+ alt="Grid and solution of the ninth cycle with contour lines." width="507" height="507">
+ </div>
+</div>
// the origin, created in the same way as shown in step-6. The mesh is
// globally refined twice followed later on by several adaptive cycles:
GridGenerator::hyper_ball (triangulation);
- static const SphericalManifold<dim> boundary;
- triangulation.set_all_manifold_ids_on_boundary(0);
- triangulation.set_manifold (0, boundary);
triangulation.refine_global(2);
// The Newton iteration starts next. During the first step we do not have