A posteriori error estimates for a finite element approximation of transmission problems with sign changing coefficients

TL;DR

This paper develops residual-based a posteriori error estimates for finite element solutions of transmission problems with sign-changing coefficients, demonstrating reliability and efficiency through numerical tests.

Contribution

It extends the a posteriori error analysis framework to discrete problems with sign-changing coefficients on regular meshes, building on previous work.

Findings

Estimator is reliable and efficient

The analysis applies to any regular mesh

Numerical tests confirm theoretical results

Abstract

We perform the a posteriori error analysis of residual type of a transmission problem with sign changing coefficients. According to [6] if the contrast is large enough, the continuous problem can be transformed into a coercive one. We further show that a similar property holds for the discrete problem for any regular meshes, extending the framework from [6]. The reliability and efficiency of the proposed estimator is confirmed by some numerical tests.