A Posterior Error Estimator for Mixed Interior Penalty Discontinuous Galerkin Finite Element Method for the H(curl)-Elliptic Problems

TL;DR

This paper introduces a novel residual-based a posteriori error estimator for mixed interior penalty discontinuous Galerkin methods applied to H(curl)-elliptic problems, with proven reliability and efficiency, validated through numerical experiments.

Contribution

It is the first to develop a residual type a posteriori error estimator for this specific method and problem class, enhancing adaptive mesh refinement.

Findings

The estimator is both reliable and efficient.

Numerical experiments confirm improved adaptive refinement.

The method advances error control in H(curl)-elliptic problems.

Abstract

In this paper, we design the first residual type a posteriori error estimator for mixed interior penalty discontinuous Galerkin method for the H(curl)-elliptic problems. Then we prove that our residual based a posteriori error indicator is both reliable and efficient. At last, we present some numerical experiments to validate the performance of the indicator within an adaptive mesh refinement procedure.