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Volume 26, Issue 2
A Posteriori Error Estimates for the Weak Galerkin Finite Element Methods on Polytopal Meshes

Hengguang Li, Lin Mu & Xiu Ye

DOI: 10.4208/cicp.OA-2018-0058

Commun. Comput. Phys., 26 (2019), pp. 558-578.

Published online: 2019-04

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  • 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.

  • Keywords

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

  • AMS Subject Headings

65N15, 65N30, 35J50

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CiCP-26-558, author = {Hengguang Li, Lin Mu and Xiu Ye}, title = {A Posteriori Error Estimates for the Weak Galerkin Finite Element Methods on Polytopal Meshes}, journal = {Communications in Computational Physics}, year = {2019}, volume = {26}, number = {2}, pages = {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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2018-0058}, url = {http://global-sci.org/intro/article_detail/cicp/13102.html} }
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 -

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.

Hengguang Li, Lin Mu and Xiu Ye. (2019). A Posteriori Error Estimates for the Weak Galerkin Finite Element Methods on Polytopal Meshes. Communications in Computational Physics. 26 (2). 558-578. doi:10.4208/cicp.OA-2018-0058
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