A Meyers type regularity result for approximations of second order elliptic operators by Galerkin schemes

TL;DR

This paper establishes a Meyers type regularity estimate for Galerkin approximations of second order elliptic operators, utilizing Sobolev space interpolation on graphs, and extends results to general graph structures.

Contribution

It introduces a Meyers type regularity estimate for Galerkin solutions of elliptic equations and generalizes estimates to broad graph settings.

Findings

Meyers type regularity estimates for Galerkin solutions

Interpolation results for Sobolev spaces on graphs

Extension of elliptic operator estimates to general graphs

Abstract

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.