Weak Galerkin based a posteriori error estimates for second order elliptic interface problems on polygonal meshes

Abstract

In this paper, we present a posteriori error estimate of weak Galerkin (WG) finite element methods based on the second order elliptic interface problems. This estimate can be applied to polygonal meshes or meshes with hanging nodes. The reliability and efficiency of the designed error estimator has been proved in this work. Extensive numerical tests are performed to validate our algorithm. These results demonstrate the effectiveness of the adaptive mesh refinement guided by the proposed error estimator.