Approximation of elliptic equations with BMO coefficients

TL;DR

This paper investigates finite element methods for elliptic equations with BMO coefficients, demonstrating convergence under certain conditions related to the oscillation of the coefficients and the function space of the right-hand side.

Contribution

It establishes convergence results for finite element schemes solving elliptic equations with BMO coefficients, a class of coefficients with limited regularity.

Findings

Finite element scheme converges for |p-2|<ε

Convergence depends on the oscillation of BMO coefficients

Applicable for right-hand sides in W^{-1}_p space

Abstract

We study solution techniques for elliptic equations in divergence form, where the coefficients are only of bounded mean oscillation (BMO). For $|p-2|<\varepsilon$ and a right hand side in $W^{-1}_p$ we show convergence of a finite element scheme, where $\varepsilon$ depends on the oscillation of the coefficients.