A Posteriori Error Estimates for a Modified Weak Galerkin Finite Element Approximation of Second Order Elliptic Problems with DG Norm

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

Yuping Zeng

Feng Wang

Zhifeng Weng

Hanzhang Hu