-----BEGIN PGP SIGNED MESSAGE----- Hash: SHA1 On 02/06/15 17:20, Jed Brown wrote: > Lawrence Mitchell <lawrence.mitch...@imperial.ac.uk> writes: >>> So the mass matrix for CG1+DG0 is singular? >> >> I believe so, yes. > > Fabulous. Now let's take a one element domain. What is the norm > of the vector > > u=((1,1,1),(-1)) > > in the "basis" {CG1, DG0}? Note that this represents the > continuous function u(x,y)=0. > > I assume FEniCS is not using QR to solve the under-determined > system, so are they silently pinning (e.g., remove the DG0 part > from one element in the domain)? If they are just "solving" the > under-determined systems by hoping that the solver doesn't notice > that the system is singular, rather than rigorously finding a > minimum norm solution (expensive), then the discrete solution can > vary an arbitrary amount by the choice of algebraic solver.
Maybe Justin can chime in here, I don't know, I just happened to know how the fenics implementation produces the "basis", so proffered that. > Why does it appear that none of the papers talk about these > issues? Pass. Lawrence -----BEGIN PGP SIGNATURE----- Version: GnuPG v1 iQEcBAEBAgAGBQJVbd76AAoJECOc1kQ8PEYvaUUH/AoKpZCNISMHrpGWNbZ67aCd 7mBJyPk7z0S7BLDeSm8i1iF+LitnzaxFNZEaGmSDWjlr1Z9tG2vjRk1R0Aj2cte+ Pb1Ki8pwdU+N1bJgV5GCW+lyaXI3QQQs2K3vsUA530ohwpPUNRqHaW4BB+IIR0hs d/vzIPEn4K9tF5JpFGMKZhJ8zuayI0NdGQ6dVqRTCxGGhTCNuOKgB9xonecHUxFg ZosuoQAVOzgbIJunJutekydvrKKpSf0I6z6cTjp713lR5cVnrGyN6J5evI9Jt7x1 Sdtczorz+EcbQ5lycBMxEGmWKIHCOM5kBG+IxjN+pQg6R/+TDbsIQL9Lyj0BU6I= =irr/ -----END PGP SIGNATURE-----