Coefficient-Robust A Posteriori Error Estimation for H(curl)-elliptic Problems

TL;DR

This paper develops a new a posteriori error estimator for H(curl)-elliptic interface problems that remains reliable despite coefficient variations, improving error control in computational electromagnetics.

Contribution

It extends existing error estimation frameworks to handle two-phase interface problems with robustness against coefficient changes.

Findings

Provides two-sided bounds for discretization error.

Demonstrates robustness with respect to coefficient variation.

Numerically compares with previous estimators for constant coefficients.

Abstract

We extend the framework of a posteriori error estimation by preconditioning in [Li, Y., Zikatanov, L.: Computers \& Mathematics with Applications. \textbf{91}, 192-201 (2021)] and derive new a posteriori error estimates for H(curl)-elliptic two-phase interface problems. The proposed error estimator provides two-sided bounds for the discretization error and is robust with respect to coefficient variation under mild assumptions. For H(curl) problems with constant coefficients, the performance of this estimator is numerically compared with the one analyzed in [Sch\"oberl, J.: Math.~Comp. \textbf{77}(262), 633-649 (2008)].