A posteriori error estimate for a WG method of H(curl)-elliptic problems

Abstract

This paper presents a posteriori error estimate for the weak Galerkin (WG) finite element method used to solve H (curl)-elliptic problems. Firstly, we introduce a WG method for solving H (curl)-elliptic problems and a corresponding residual type error estimator without a stabilization term. Secondly, we establish the reliability of the error estimator by demonstrating that the stabilization term is controlled by the error estimator. We also evaluate the efficiency of the error estimator using standard bubble functions. Finally, we present some numerical results to show the performances of the error estimator in both uniform and adaptive meshes.