Jed, I am not quite sure what you're asking for. Are you asking for how people actually implement this augmented TH? In other words, how the shape/basis functions for this mixed function space would look? I have only seen in some key note lectures and presentations at conferences briefly mentioning this P2/(P1+P0) element, as if it's the de facto discretization for Stokes flows. That said, even I am not too sure how this would look.
Matt, In the 'quad_q2p1_full' example you pointed me to, is that P2/P1_disc or P2/(P1+P0)? I imagine those are two very different discretizations, so when you have the command line option "-pres_petscdualspace_lagrange_continuity 0" it looks to me you're doing the former? Thanks, Justin On Mon, Jun 1, 2015 at 10:02 AM, Matthew Knepley <[email protected]> wrote: > On Mon, Jun 1, 2015 at 9:38 AM, Jed Brown <[email protected]> wrote: > >> Justin Chang <[email protected]> writes: >> >> > 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). >> >> This analysis does not state a finite element. > > > They certaiinly state the approximation space up front. Then later in the > paper > they say that they independently test with P1 and P0, and that this has a > 1D > null space, and then in the solution section they have some way of > handling that > which I ignored because its easy to handle. > > Matt > > >> > 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), >> >> Could you point to a specific example? How are they handling >> linear dependence of the "basis"? >> > > > > -- > What most experimenters take for granted before they begin their > experiments is infinitely more interesting than any results to which their > experiments lead. > -- Norbert Wiener >
