There is no graphical output for this step so this is easy.
@code
Using mapping with degree 1:
============================
-cells |u|_1 error
- 5 0.680402 0.572912
- 20 1.085518 0.167796
- 80 1.208981 0.044334
- 320 1.242041 0.011273
- 1280 1.250482 0.002832
- 5120 1.252605 0.000709
+cells |u|_1 error
+ 5 0.680402 0.572912
+ 20 1.088141 0.165173
+ 80 1.210142 0.043172
+ 320 1.242375 0.010939
+ 1280 1.250569 0.002745
+ 5120 1.252627 0.000687
Using mapping with degree 2:
============================
-cells |u|_1 error
- 5 1.050963 0.202351
- 20 1.199642 0.053672
- 80 1.239913 0.013401
- 320 1.249987 0.003327
- 1280 1.252486 0.000828
- 5120 1.253108 0.000206
+cells |u|_1 error
+ 5 1.177062 0.076252
+ 20 1.228978 0.024336
+ 80 1.245175 0.008139
+ 320 1.250881 0.002433
+ 1280 1.252646 0.000668
+ 5120 1.253139 0.000175
Using mapping with degree 3:
============================
-cells |u|_1 error
- 5 1.086161 0.167153
- 20 1.204349 0.048965
- 80 1.240502 0.012812
- 320 1.250059 0.003255
- 1280 1.252495 0.000819
- 5120 1.253109 0.000205
+cells |u|_1 error
+ 5 1.193493 0.059821
+ 20 1.229825 0.023489
+ 80 1.245221 0.008094
+ 320 1.250884 0.002430
+ 1280 1.252646 0.000668
+ 5120 1.253139 0.000175
@endcode
As we expected, the convergence order for each of the different
mappings is clearly quadratic in the mesh size. What <em>is</em>
void LaplaceProblem<dim>::run ()
{
GridGenerator::hyper_ball (triangulation);
- static const SphericalManifold<dim> boundary;
- triangulation.set_all_manifold_ids_on_boundary(0);
- triangulation.set_manifold (0, boundary);
for (unsigned int cycle=0; cycle<6; ++cycle, triangulation.refine_global(1))
{
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