A Posteriori Error Estimates for a Modified Weak Galerkin Finite Element Approximation of Second Order Elliptic Problems with DG Norm
Year: 2021
Author: Yuping Zeng, Feng Wang, Zhifeng Weng, Hanzhang Hu
Journal of Computational Mathematics, Vol. 39 (2021), Iss. 5 : pp. 755–776
Abstract
In this paper, we derive a residual based a posteriori error estimator for a modified weak Galerkin formulation of second order elliptic problems. We prove that the error estimator used for interior penalty discontinuous Galerkin methods still gives both upper and lower bounds for the modified weak Galerkin method, though they have essentially different bilinear forms. More precisely, we prove its reliability and efficiency for the actual error measured in the standard DG norm. We further provide an improved a priori error estimate under minimal regularity assumptions on the exact solution. Numerical results are presented to verify the theoretical analysis.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.2006-m2019-0010
Journal of Computational Mathematics, Vol. 39 (2021), Iss. 5 : pp. 755–776
Published online: 2021-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 22
Keywords: Modified weak Galerkin method A posteriori error estimate A medius error analysis.
Author Details
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https://doi.org/10.1016/j.camwa.2023.04.028 [Citations: 0]