We prove a Meyers type regularity estimate for approximate solutions of second order elliptic equations obtained by Galerkin methods. The proofs rely on interpolation results for Sobolev spaces on graphs. Estimates for second order elliptic operators on rather general graphs are also obtained.
@article{arxiv.1201.6332,
title = {A Meyers type regularity result for approximations of second order elliptic operators by Galerkin schemes},
author = {Nadine Badr and Emmanuel Russ},
journal= {arXiv preprint arXiv:1201.6332},
year = {2012}
}