Dear Torquil,
The resulting finite element space when you supress the dof corresponding to intermediate points is not a partition of unity. So, it is not able to approximate the constants. Consequently, I think, it is normal that the solution is not well approximated. You have at least to care that your reduction produces a finite element space which reproduces the polynomial of degree less or equal to 1 to have a good approximation. Yves. Le 15/07/2012 15:56, Torquil Macdonald Sørensen a écrit : > Hi! > > I've started with the tests/laplacian.cc program, modified it a bit, > and implemented an example reduction scheme. But whenever I use > reduction, the solution is identical to zero apart from on the > boundary, where I use Dirichlet conditions. In addition, I've also > tried an approach using the Laplacian model, with the same incorrect > results. > > In more detail, I have a square 2d domain and the mesh is: > > getfem::regular_unit_mesh(mesh, ref, bgeot::parallelepiped_geotrans(2, > 1)); > > On this mesh, I'm using FEM_QK(2,2) for both parts of the equation, > and IM_GAUSS_PARALLELEPIPED(2,k) for k=3, but I've also tried k=4 and 5. > > The reduction scheme consists of using only the DOFs at the corners of > the squares, and not the DOFs at the intermediate points along the > edges or the central point of the square. I thought I'd try this as a > simple example of reduction. The extention matrix E is the transpose > of the reduction matrix R, and I do test that R*E is the identity, so > that part should be OK. > > When using reduction, I make sure to use the "general Dirichlet" > method in laplacian.cc, since the simplified approach won't work in > that case. > > The program runs fine without error messages with and without > reduction enabled, but as I mentioned, the solution is incorrect when > using reduction (zero everywhere apart from the boundary). > > Any ideas about why this is so? Perhaps my reduction scheme is > mathematically invalid for some reason, there is some bug in > connection with reduction, or I've done something wrong? > > Best regards, > Torquil Sørensen > > > _______________________________________________ > Getfem-users mailing list > [email protected] > https://mail.gna.org/listinfo/getfem-users -- Yves Renard ([email protected]) tel : (33) 04.72.43.87.08 Pole de Mathematiques, INSA-Lyon fax : (33) 04.72.43.85.29 20, rue Albert Einstein 69621 Villeurbanne Cedex, FRANCE http://math.univ-lyon1.fr/~renard --------- _______________________________________________ Getfem-users mailing list [email protected] https://mail.gna.org/listinfo/getfem-users
