TY - JOUR
T1 - A Posteriori Error Estimates for the Weak Galerkin Finite Element Methods on Polytopal Meshes
AU - Hengguang Li, Lin Mu & Xiu Ye
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 - <p style="text-align: justify;">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.</p>