## Re: [Libmesh-users] WARNING: Second derivatives are not currently correctly calculated on non-affine elements!

 Re: [Libmesh-users] WARNING: Second derivatives are not currently correctly calculated on non-affine elements! From: Roy Stogner - 2011-07-12 06:30:06 ```On Mon, 11 Jul 2011, Ataollah Mesgarnejad wrote: > Can anyone please instruct me on elements and FE types that I can > use for second order problems? As part of my code solves biharmonic > equation. I get the warning: Any FE type will give you second derivatives, but the results will only be L2 integrable for the CLOUGH and HERMITE (i.e. our C1) elements. Try to do a fourth-order problem with anything else we have and you'll need to use a discontinuous or semi-discontinuous formulation. > WARNING: Second derivatives are not currently correctly calculated on non-affine elements! > > when I try to run my code on some of my meshes. The HERMITE elements are very restrictive: they basically require your elements to be parallelograms in 2D or parallelepipeds in 3D. For any other element, the restriction is that the master->physical element mapping has to be an affine map: (x,y,z) = A * (xi,eta,zeta) + b for some tensor A and vector b. For quad/hex elements that boils down to parallelograms/parallelepipeds again; for triangles and tets anything with all straight edges will work. We'd love to get a patch implementing more flexible C1 quad/hex elements, and/or a patch which calculates the second derivative terms we currently neglect on non-affine elements, but generally anyone who would benefit from such features is wise and/or lazy enough to switch to straight-edged tri/tet meshes instead. --- Roy ```

### Thread view

 [Libmesh-users] WARNING: Second derivatives are not currently correctly calculated on non-affine elements! From: Ataollah Mesgarnejad - 2011-07-12 02:59:34 ```Dear all, Can anyone please instruct me on elements and FE types that I can use for second order problems? As part of my code solves biharmonic equation. I get the warning: WARNING: Second derivatives are not currently correctly calculated on non-affine elements! when I try to run my code on some of my meshes. Best, Ata ```
 Re: [Libmesh-users] WARNING: Second derivatives are not currently correctly calculated on non-affine elements! From: Roy Stogner - 2011-07-12 06:30:06 ```On Mon, 11 Jul 2011, Ataollah Mesgarnejad wrote: > Can anyone please instruct me on elements and FE types that I can > use for second order problems? As part of my code solves biharmonic > equation. I get the warning: Any FE type will give you second derivatives, but the results will only be L2 integrable for the CLOUGH and HERMITE (i.e. our C1) elements. Try to do a fourth-order problem with anything else we have and you'll need to use a discontinuous or semi-discontinuous formulation. > WARNING: Second derivatives are not currently correctly calculated on non-affine elements! > > when I try to run my code on some of my meshes. The HERMITE elements are very restrictive: they basically require your elements to be parallelograms in 2D or parallelepipeds in 3D. For any other element, the restriction is that the master->physical element mapping has to be an affine map: (x,y,z) = A * (xi,eta,zeta) + b for some tensor A and vector b. For quad/hex elements that boils down to parallelograms/parallelepipeds again; for triangles and tets anything with all straight edges will work. We'd love to get a patch implementing more flexible C1 quad/hex elements, and/or a patch which calculates the second derivative terms we currently neglect on non-affine elements, but generally anyone who would benefit from such features is wise and/or lazy enough to switch to straight-edged tri/tet meshes instead. --- Roy ```
 Re: [Libmesh-users] WARNING: Second derivatives are not currently correctly calculated on non-affine elements! From: Roy Stogner - 2011-07-12 14:40:02 ```On Tue, 12 Jul 2011, Ataollah Mesgarnejad wrote: > So here's the catch I need C^0 continuity but I also need access to > face information on elements. I assumed that this can be done just > using usual C^0 (not monomial or XYZ ) and updating face information > right ? Yes. Two things to watch out for: you'll also want side information from a neighboring element at the *original* element's side quadrature points, and you'll want to only integrate each side once. See our DG example or the jump error estimator code for examples of how to handle all that. --- Roy ```

## Get latest updates about Open Source Projects, Conferences and News.

Sign up for the SourceForge newsletter:

No, thanks