A finite element method for high-contrast interface problems with error estimates independent of contrast

TL;DR

This paper introduces a finite element method for elliptic interface problems with high contrast in coefficients, achieving error estimates that are independent of the contrast, validated through theoretical analysis and numerical experiments.

Contribution

A novel finite element approach that provides contrast-independent error estimates for high-contrast interface problems with non-aligned meshes.

Findings

Optimal error estimates in $L^2$ and $H^1$ norms independent of contrast

Method validated by numerical experiments

Applicable to problems with discontinuous diffusion coefficients

Abstract

We define a new finite element method for a steady state elliptic problem with discontinuous diffusion coefficients where the meshes are not aligned with the interface. We prove optimal error estimates in the $L^2$ norm and $H^1$ weighted semi-norm independent of the contrast between the coefficients. Numerical experiments validating our theoretical findings are provided.