There are a few papers that discuss this modified/augmented Taylor-Hood elements for Stokes equations in detail (e.g., http://link.springer.com/article/10.1007%2Fs10915-011-9549-4). From what I have seem, it seems people primarily use this to ensure local mass conservation while attaining the desirable qualities of the TH element. Lately I have seen this element used in many FEniCS and Deal.II applications (and it's also very easy to implement, just a few additional lines of code), which is why I had wanted to experiment with this myself (if possible) using DMPlex.
On Sun, May 31, 2015 at 7:59 PM, Jed Brown <[email protected]> wrote: > Justin Chang <[email protected]> writes: > > > I am referring to P2 / (P1 + P0) elements, I think this is the correct > way > > of expressing it. Some call it modified Taylor Hood, others call it > > something else, but it's not Crouzeix-Raviart elements. > > Okay, thanks. This pressure space is not a disjoint union (the constant > exists in both spaces) and thus the obvious "basis" is actually not > linearly independent. I presume that people using this element do some > "pinning" (like set one cell "average" to zero) instead of enforcing a > unique expression via a Lagrange multiplier (which would involve a dense > row and column). That may contribute to ill conditioning and in any > case, would make domain decomposition or multigrid preconditioners more > technical. Do you know of anything explaining why the method is not > very widely used (e.g., in popular software packages, finite element > books, etc.)? >
