Hi Arthur, Thank you for reporting this! This is another simplex bug inside deal.II. From 1999ish until 2021 we assumed 2d grids had consistently oriented lines, but this cannot be enforced in for triangles in 2d, and over the last two years I've been fixing a long tail of minor bugs related to this assumption. I have a patch which fixes this here:
https://github.com/dealii/dealii/pull/18832 I gave you credit for figuring this one out in the changelog. Best, David Wells ________________________________ From: [email protected] <[email protected]> on behalf of [email protected] <[email protected]> Sent: Wednesday, August 20, 2025 9:56 AM To: deal.II User Group <[email protected]> Subject: [deal.II] Re: Convergence issues for cubic FE_SimplexP on triangles 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]<mailto:[email protected]>. To view this discussion visit https://groups.google.com/d/msgid/dealii/2d16fa24-b5f7-4ddd-9714-19da192846bcn%40googlegroups.com<https://groups.google.com/d/msgid/dealii/2d16fa24-b5f7-4ddd-9714-19da192846bcn%40googlegroups.com?utm_medium=email&utm_source=footer>. -- 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/SA1PR03MB6387E4CE12DC39990517F8E3ED33A%40SA1PR03MB6387.namprd03.prod.outlook.com.
