Elliptic and Parabolic Equations - Abstract

Glitzky, Annegret

Discrete Sobolev--Poincaré inequalities using the $W^1,p$ seminorm in the setting of Voronoi finite volume approximations

We present discrete Poincaré and Sobolev-Poincaré inequalities for functions with arbitrary boundary values on Voronoi finite volume meshes. Our results include the non-Hilbertian case ($pneq 2$), too. We use Sobolev's integral representation and estimate weakly singular integrals in the context of Voronoi finite volumes.