On 30/10/2018 20:04, Stogner, Roy H wrote: > On Tue, 30 Oct 2018, Hubert Weissmann wrote: > >> On 30.10.2018 16:50, John Peterson wrote: >>> On Tue, Oct 30, 2018 at 9:28 AM Hubert Weissmann >>> <hubert.weissm...@gmail.com <mailto:hubert.weissm...@gmail.com>> wrote: >>> >>> Dear all, >>> >>> I have trouble with the regularity of my solution (using >>> Lagrange-elements, only continuity is ensured), and therefore >>> thinking >>> whether I should switch to Clough-Tocher elements or Hermite elements. >>> >>> >>> Are you solving a problem (e.g. biharmonic equation) where you expect the >>> solution to be in C^1? >> I forgot to mention: I am solving the laplace equation. >> In principle I expect my solution to be at least in C^2; so any improvement >> of the continuity is appreciated. > To be fair, you're still getting the wrong answer with either element, > so you have room to play: If you wanted improved continuity out of > Lagrange, you can postprocess to get it. > > But an advantage of the Hermites is that because you're *not* > postprocessing you basically "save DoFs" by not wasting them on > derivative discontinuities you expect not to exist. So you end up > using ~8 DoFs per element for cubics in 3D instead of ~27 DoFs per, > and yet you don't lose much accuracy by it. IMHO this sort of "k" > refinement that increases smoothness ought to go hand in hand with p > refinement, except that most software isn't set up to make that easy. > If you know you're never going to be applying non-smooth forcing > functions or boundary conditions then asking for more continuity > uniformly is still tempting. Yes, that is at least my hope. Moreover, I have the impression that the kinks introduce some global error, as the behaviour of the solution strongly depends on the exact position of that kink; so I am not sure whether postprocessing can help me very much. >> In principle, I agree with you; in the FE-region, it looks quite fine with >> Lagrange elements. But since the boundary to infinite elements is really >> bad, >> I hope to improve with other elements. >> The main disadvantage is that none of them are implemented for infinite >> elements nor for Tets, which I use since they are much easier to setup; but >> I >> might change this... > If you're mixing them with infinite elements, then the main > disadvantage I see is that it's going to be impossible for you to > handle the domain! IIRC currently the HERMITE element type requires > your elements' xi/eta/zeta axes to line up everywhere with x/y/z (e.g. > you're forced to use rectangles in 2D), and even in principle the way > they handle mixed derivatives requires you to have continuous edges > going through nodes (e.g. you have to be working on a diffeomorphism > from a grid of squares); but that means you're going to have at least > 4 square corners on the edges of your FE boundary, and that means the > InfFE approximation extending from those corners is going to be lousy, > isn't it?
I must admit that I didn't look closely at the current implementation; I just saw that the elements I would like to use are not done, so far. Is there a strict reason why the elements must align with the axes? I have smooth parameters and driving forces, but my elements are rather arbitrary and roughly align in spheres. There are people who actually use InfFE with a 'rectangular' interface, but I would actually like to avoid it... Are the Clough-elements more promising? Hubert > --- > Roy _______________________________________________ Libmesh-users mailing list Libmesh-users@lists.sourceforge.net https://lists.sourceforge.net/lists/listinfo/libmesh-users
