Dear Arthur, Thank you for the very thorough and detailed question. I'll look into and try to get back to you (or at least try to reach out to people that might have a clearer idea). If that can reassure you, I have tried to reproduce your results using Lethe and I get the same conclusion to you regarding convergence of P3 triangles. I'll look into it and ask around. Might take a small while, but I am on it :)
On Friday, August 15, 2025 at 6:45:17 p.m. UTC+2 [email protected] wrote: > Good morning deal.ii developers, > > I was doing convergence tests with a manufactured solution with simplicial > meshes and did not obtain the expected convergence with cubic elements on > triangles (FE_SimplexP<2>(3)). I wrote a very simple interpolation > convergence test to check: on tetrahedra, all degrees converge with the > expected rates in L2, Linf and H1 (semi)norms; on triangles the results are > good for P1 and P2 on triangles, but not for P3, where I get first order > convergence for L2, Linf and no convergence in H1: > > P1 on triangles > Number of dofs: 25 > Number of dofs: 81 > Number of dofs: 289 > Number of dofs: 1089 > nElm L2_u Li_u H1_u > 32 5.938414e-03 - - 2.425255e-02 - - 1.549249e-01 - - > 128 1.498810e-03 3.96 1.99 6.769010e-03 3.58 1.84 7.782930e-02 1.99 0.99 > 512 3.755853e-04 3.99 2.00 1.780487e-03 3.80 1.93 3.896037e-02 2.00 1.00 > 2048 9.395142e-05 4.00 2.00 4.561509e-04 3.90 1.96 1.948590e-02 2.00 1.00 > > P2 on triangles > Number of dofs: 81 > Number of dofs: 289 > Number of dofs: 1089 > Number of dofs: 4225 > nElm L2_u Li_u H1_u > 32 3.112575e-04 - - 6.997055e-04 - - 1.041667e-02 - - > 128 3.890718e-05 8.00 3.00 8.746319e-05 8.00 3.00 2.604167e-03 4.00 2.00 > 512 4.863398e-06 8.00 3.00 1.093290e-05 8.00 3.00 6.510417e-04 4.00 2.00 > 2048 6.079247e-07 8.00 3.00 1.366612e-06 8.00 3.00 1.627604e-04 4.00 2.00 > > P3 on triangles > Number of dofs: 169 > Number of dofs: 625 > Number of dofs: 2401 > Number of dofs: 9409 > nElm L2_u Li_u H1_u > 32 1.541667e-02 - - 7.120958e-02 - - 5.117887e-01 - - > 128 8.815536e-03 1.75* 0.81* 4.355310e-02 1.64* 0.71* 5.712863e-01 0.90* > -0.16* > 512 4.690321e-03 1.88 *0.91* 2.389578e-02 1.82* 0.87* 6.001976e-01 0.95* > -0.07* > 2048 2.416438e-03 1.94 *0.96* 1.249422e-02 1.91 *0.94* 6.144240e-01 0.98* > -0.03* > > P1 on tets > Number of dofs: 125 > Number of dofs: 729 > Number of dofs: 4913 > Number of dofs: 35937 > nElm L2_u Li_u H1_u > > 384 8.095068e-03 - - 6.562605e-02 - - 1.735667e-01 - > - > 3072 2.289416e-03 3.54 1.82 2.693394e-02 2.44 1.28 9.615581e-02 1.81 > 0.85 > 24576 5.896877e-04 3.88 1.96 7.780330e-03 3.46 1.79 4.927053e-02 1.95 > 0.96 > 196608 1.485159e-04 3.97 1.99 2.081313e-03 3.74 1.90 2.478494e-02 1.99 > 0.99 > > P2 on tets > Number of dofs: 729 > Number of dofs: 4913 > Number of dofs: 35937 > Number of dofs: 274625 > nElm L2_u Li_u H1_u > > 384 1.118739e-03 - - 1.184543e-02 - - 2.361912e-02 - > - > 3072 1.637572e-04 6.83 2.77 3.376606e-03 3.51 1.81 6.731956e-03 3.51 > 1.81 > 24576 2.117353e-05 7.73 2.95 4.535571e-04 7.44 2.90 1.732030e-03 3.89 > 1.96 > 196608 2.668408e-06 7.93 2.99 5.866221e-05 7.73 2.95 4.360374e-04 3.97 > 1.99 > > P3 on tets > Number of dofs: 2197 > Number of dofs: 15625 > Number of dofs: 117649 > Number of dofs: 912673 > nElm L2_u Li_u H1_u > > 384 1.074553e-04 - - 7.422949e-04 - - 2.346755e-03 - > - > 3072 8.111057e-06 13.25 *3.73* 1.300853e-04 5.71 *2.51* 3.362943e-04 > 6.98* 2.80* > 24576 5.264880e-07 15.41 *3.95* 8.130328e-06 16.00 *4.00* 4.327503e-05 > 7.77 *2.96* > 196608 3.320390e-08 15.86 *3.99* 5.081455e-07 16.00 *4.00* 5.447386e-06 > 7.94 > * 2.99* > > Is there something that I'm doing wrong, or is it just a bug somewhere in > FE_SimplexP? > I have joined a MWE with the 2D and 3D meshes (in .msh4 format). > > Thank you for your help, and thanks a lot for developing the library! > Arthur Bawin > > -- The deal.II project is located at http://www.dealii.org/ For mailing list/forum options, see https://groups.google.com/d/forum/dealii?hl=en --- You received this message because you are subscribed to the Google Groups "deal.II User Group" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion visit https://groups.google.com/d/msgid/dealii/2d16fa24-b5f7-4ddd-9714-19da192846bcn%40googlegroups.com.
