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Volume 39, Issue 5
A Posteriori Error Estimates for a Modified Weak Galerkin Finite Element Approximation of Second Order Elliptic Problems with DG Norm

Yuping Zeng, Feng Wang, Zhifeng Weng & Hanzhang Hu

DOI: 10.4208/jcm.2006-m2019-0010

J. Comp. Math., 39 (2021), pp. 755-776.

Published online: 2021-08

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  • 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.

  • Keywords

Modified weak Galerkin method, A posteriori error estimate, A medius error analysis.

  • AMS Subject Headings

65N15, 65N30

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

zeng_yuping@163.com (Yuping Zeng)

fwang@njnu.edu.cn (Feng Wang)

zfwmath@163.com (Zhifeng Weng)

huhanzhang1016@163.com (Hanzhang Hu)

  • BibTex
  • RIS
  • TXT
@Article{JCM-39-755, author = {Zeng , YupingWang , FengWeng , Zhifeng and Hu , Hanzhang}, title = {A Posteriori Error Estimates for a Modified Weak Galerkin Finite Element Approximation of Second Order Elliptic Problems with DG Norm}, journal = {Journal of Computational Mathematics}, year = {2021}, volume = {39}, number = {5}, pages = {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.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.2006-m2019-0010}, url = {http://global-sci.org/intro/article_detail/jcm/19383.html} }
TY - JOUR T1 - A Posteriori Error Estimates for a Modified Weak Galerkin Finite Element Approximation of Second Order Elliptic Problems with DG Norm AU - Zeng , Yuping AU - Wang , Feng AU - Weng , Zhifeng AU - Hu , Hanzhang JO - Journal of Computational Mathematics VL - 5 SP - 755 EP - 776 PY - 2021 DA - 2021/08 SN - 39 DO - http://doi.org/10.4208/jcm.2006-m2019-0010 UR - https://global-sci.org/intro/article_detail/jcm/19383.html KW - Modified weak Galerkin method, A posteriori error estimate, A medius error analysis. AB -

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.

Zeng , YupingWang , FengWeng , Zhifeng and Hu , Hanzhang. (2021). A Posteriori Error Estimates for a Modified Weak Galerkin Finite Element Approximation of Second Order Elliptic Problems with DG Norm. Journal of Computational Mathematics. 39 (5). 755-776. doi:10.4208/jcm.2006-m2019-0010
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