A Posteriori Error Estimates for the Weak Galerkin Finite Element Methods on Polytopal Meshes (Communications in Computational Physics, 2019)
In this paper, we present a simple a posteriori error estimate for the weakGalerkin (WG) finite element method for a model second order elliptic equation. Thisresidual type estimator can be applied to general meshes such as hybrid, polytopaland those with hanging nodes. We prove the reliability and efficiency of the estimator. Extensive numerical tests demonstrate the effectiveness and flexibility of the meshrefinement guided by this error estimator.