On Tue, Feb 14, 2012 at 09:20, Thomas Witkowski <thomas.witkowski@tu-dresden.de> wrote:

I discretize the Laplace operator (using finite element) on the unit square equipped with periodic boundary conditions on all four edges. Is it correct that the null space is still constant? I wounder, because when I run the same code on a sphere (so a 2D surface embedded in 3D), the resulting matrix is non-singular. I thought, that both cases should be somehow equal with respect to the null space?

The continuum operators for both cases have a constant null space, so if either is nonsingular in your finite element code, it's a discretization problem.