On Fri, 4 Sep 2009, Hanjoerg Seybold wrote: > Hello, > we would like to solve a biharmonic problem on a tube. > For this we would like to use a Hex mesh (not rectilinear) > > For the Hermite elements we get the warning. > -WARNING: Second derivatives are not currently correctly calculated on > non-affine elements! > > Does this mean that Hermite elements can only be used on rectilinear/octree > meshes or just that the approximation of the boundary is not correct > in the mapping.
There are two problems that will affect you here: One is that, as you suspected, Hermite elements can only be used on rectilinear/octree meshes. Parallelepipeds should also work but haven't been tested. This is a conceptual problem with the Hermite elements themselves, not just a software limitation; the way these elements maintain continuity is to enforce equality of a few (but not all) mixed second derivative terms at nodes, and that breaks unless those terms match up from element to element. Two is that, as the library is warning you, we don't calculate second derivatives correctly on curved elements. This is just a software limitation; I was only running problems on polygonal and rectilinear meshes when I added the second derivative support, so I lazily avoided adding the extra terms that would come from non-affine geometric mappings. The way to handle fourth-order problems on general 3D domains would be to add these terms and to also add a class of general C1 3D elements. If you're motivated enough to do this, I will be thrilled. But if you're as lazy as I am, and if your domains are all simple tubes, the easier way to do things would be to recast your problem in polar coordinates, then solve it on a rectilinear domain with periodic boundary conditions. --- Roy ------------------------------------------------------------------------------ Let Crystal Reports handle the reporting - Free Crystal Reports 2008 30-Day trial. Simplify your report design, integration and deployment - and focus on what you do best, core application coding. Discover what's new with Crystal Reports now. http://p.sf.net/sfu/bobj-july _______________________________________________ Libmesh-users mailing list [email protected] https://lists.sourceforge.net/lists/listinfo/libmesh-users
