A recovery-based a posteriori error estimator of the weak Galerkin finite element method for elliptic problems

Abstract In this paper, we propose a recovery-type a posteriori error estimator of the weak Galerkin finite element method for the second order elliptic equation. The reliability and efficiency of the estimator are analyzed by a discrete  H 1 -norm of the exact error. The estimator is further used in the adaptive weak Galerkin algorithm on the triangular, quadrilateral and other polygonal meshes. Numerical results are provided to demonstrate the effectiveness of the adaptive mesh refinement guided by this estimator.