Hi everyone! I am trying to implement the stabilizations presented in a paper by Bochev et al. [2006], which you may find here:
https://pdfs.semanticscholar.org/47be/4e317d4dcbbf1b70c781394e49c1dbf7e538.pdf This one is parameter free, and they present local projections for both Q1Q1 and Q1Q0 element pairs (both of course not fulfillling the LBB cond). The Q1Q1 is easily implemented, since we only need to adapt the cell matrices, but this would also be possible with the PSPG stabilization for example, nevertheless, here we do not need a parameter. More interestingly, the Q1Q0 pair allows the use of discontinuous pressure, which is in my case of interest, since I want to finally apply this to a ALE-FSI approach, where at the interface the pressure is discontinuous. -And for the PSPG I need the derivatives of the pressure functions, wihch are exactly zero for continuous functions mapped by affine mappings (which is for quads/hexas of course most likely not the case). FINALLY, MY QUESTIONS: Using the Q1Q1, I would in the end (FSI) need to come up with a space made from Q1 elements with a discontinuity at the interface - which shall be realized using different material_id(). - how may I do that other than using a FE_DGQ space for the pressure and enforce continuity 'manually' through a giant ConstraintMatrix? Using the Q1Q0, the main problem is data transfer and 'node searching' in the parallel case - example: the stabilization matrix from cell 16 has pressure dof 45 and shares edges or maybe only a single vertex (!) with cells with pressure dofs 1 2 3 4 5. The cell matrix for the projection from Q0(dc) to Q1(c) is an area-weighted sum of the pressures on the cells touching the vertex of the support of the matching bilinear function, therefore we get a 6x6 local matrix and entries into all 'touching' cells. Since these cells are not only the direct neighbors of the current cell, things may get complicated quite fast, if we consider the 3d case with hanging nodes, but on the other hand side, looping in the element loop over all elements again(!) to check the vertex_index() is extremely slow. - Is there a fast and efficient way to get the 'touching' cells in a triangulation for one vertex? (of course i do that only once during setup and save a std::map from active_cell_index to pressure dof and cell area) Do you know of any better-fitting stabilizations for the Q1Q0 pair? Or do you think there are better options around? Any help would be greatly appreciated! Thanks in advance! Kind regards, Richard -- 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/f98bf7c9-ed79-43b5-bf70-d2babcecb783%40googlegroups.com.
