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A Posteriori Error Estimates for the Weak Galerkin Finite Element Methods on Polytopal Meshes

A Posteriori Error Estimates for the Weak Galerkin Finite Element Methods on Polytopal Meshes
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Year:    2019

Communications in Computational Physics, Vol. 26 (2019), Iss. 2 : pp. 558–578

Abstract

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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/cicp.OA-2018-0058

Communications in Computational Physics, Vol. 26 (2019), Iss. 2 : pp. 558–578

Published online:    2019-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    21

Keywords:    Weak Galerkin finite element methods second-order elliptic problems a posteriori error estimate polytopal meshes.

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