Hi there, I have recently implemented a hybridizable discontinuous Galerkin method for the convection-diffusion equation adapted from step-51. Instead of the LHDG method used therein, I used IPHDG.
Some major differences between the two include that IPHDG doesn't have a vector-valued auxiliary variable *q* as in step-51 and that an interior penalty term *<alpha * kappa / hK (u_h - uhat_h),(v_h - vhat_h)>* is present in IPHDG where *kappa* is the diffusion parameter, hK is the mesh size and *alpha* is the interior penalty parameter, usually set to be 4.0*p^2 (p = fe.degree). When solving an example 2D problem on a unit square domain and a uniformly refined mesh, and when using FE_DGP space paired with FE_FaceP space, things worked out fine across the board with* kappa* = 1, 1e-2, 1e-6. When FE_DGQ and FE_FaceQ are used, however, things went off the rails where I had to tune up the IP parameter *alpha *to at least 4.0*p^2/h_K to retain the correct rates of convergence. In fact, the bigger the diffusion parameter *kappa*, the earlier the instability shows which seems to confirm that the issue lies in the interior penalty term. All of this happened when I didn't change the code at all except for switching *P spaces to *Q spaces. I'm wondering whether there is anyone here who has experience with IPHDG and/or using FE_DGQ vs FE_DGP in general. Any suggestions and insights would be highly appreciated! Best regards, Greg -- 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 dealii+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/dealii/cc4d5895-4937-409b-9fea-f2186f4b2359n%40googlegroups.com.
