TY - JOUR T1 - A Posteriori Error Estimates for the Weak Galerkin Finite Element Methods on Polytopal Meshes JO - Communications in Computational Physics VL - 2 SP - 558 EP - 578 PY - 2019 DA - 2019/04 SN - 26 DO - http://doi.org/10.4208/cicp.OA-2018-0058 UR - https://global-sci.org/intro/article_detail/cicp/13102.html KW - Weak Galerkin, finite element methods, second-order elliptic problems, a posteriori error estimate, polytopal meshes. AB -

In this paper, we present a simple a posteriori error estimate for the weak Galerkin (WG) finite element method for a model second order elliptic equation. This residual type estimator can be applied to general meshes such as hybrid, polytopal and those with hanging nodes. We prove the reliability and efficiency of the estimator. Extensive numerical tests demonstrate the effectiveness and flexibility of the mesh refinement guided by this error estimator.