Discrete Sobolev--Poincaré inequalities for Voronoi finite volume approximations
- Glitzky, Annegret
- Griepentrog, Jens André
2010 Mathematics Subject Classification
- 46E35 46E39 31B10
- Discrete Sobolev inequality, Sobolev integral representation, Voronoi finite volume mesh
We prove a discrete Sobolev-Poincare inequality for functions with arbitrary boundary values on Voronoi finite volume meshes. We use Sobolev's integral representation and estimate weakly singular integrals in the context of finite volumes. We establish the result for star shaped polyhedral domains and generalize it to the finite union of overlapping star shaped domains. In the appendix we prove a discrete Poincare inequality for space dimensions greater or equal to two.
- SIAM J. Numer. Anal., 48 (2010) pp. 372--391.