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Volume 14, Issue 3
Low Regularity Error Analysis for Weak Galerkin Finite Element Methods for Second Order Elliptic Problems

Xiu Ye & Shangyou Zhang

DOI: 10.4208/nmtma.OA-2020-0120

Numer. Math. Theor. Meth. Appl., 14 (2021), pp. 613-623.

Published online: 2021-06

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  • Abstract

This paper presents error estimates in both an energy norm and the $L^2$-norm for the weak Galerkin (WG) finite element methods for elliptic problems with low regularity solutions. The error analysis for the continuous Galerkin finite element remains same regardless of regularity. A totally different analysis is needed for discontinuous finite element methods if the elliptic regularity is lower than H-1.5. Numerical results confirm the theoretical analysis.

  • Keywords

Weak Galerkin, finite element methods, weak gradient, second-order elliptic problems, low regularity.

  • AMS Subject Headings

65N15, 65N30 Secondary: 35J50

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{NMTMA-14-613, author = {Ye , Xiu and Zhang , Shangyou}, title = {Low Regularity Error Analysis for Weak Galerkin Finite Element Methods for Second Order Elliptic Problems}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2021}, volume = {14}, number = {3}, pages = {613--623}, abstract = {

This paper presents error estimates in both an energy norm and the $L^2$-norm for the weak Galerkin (WG) finite element methods for elliptic problems with low regularity solutions. The error analysis for the continuous Galerkin finite element remains same regardless of regularity. A totally different analysis is needed for discontinuous finite element methods if the elliptic regularity is lower than H-1.5. Numerical results confirm the theoretical analysis.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.OA-2020-0120}, url = {http://global-sci.org/intro/article_detail/nmtma/19191.html} }
TY - JOUR T1 - Low Regularity Error Analysis for Weak Galerkin Finite Element Methods for Second Order Elliptic Problems AU - Ye , Xiu AU - Zhang , Shangyou JO - Numerical Mathematics: Theory, Methods and Applications VL - 3 SP - 613 EP - 623 PY - 2021 DA - 2021/06 SN - 14 DO - http://doi.org/10.4208/nmtma.OA-2020-0120 UR - https://global-sci.org/intro/article_detail/nmtma/19191.html KW - Weak Galerkin, finite element methods, weak gradient, second-order elliptic problems, low regularity. AB -

This paper presents error estimates in both an energy norm and the $L^2$-norm for the weak Galerkin (WG) finite element methods for elliptic problems with low regularity solutions. The error analysis for the continuous Galerkin finite element remains same regardless of regularity. A totally different analysis is needed for discontinuous finite element methods if the elliptic regularity is lower than H-1.5. Numerical results confirm the theoretical analysis.

Xiu Ye & Shangyou Zhang. (2021). Low Regularity Error Analysis for Weak Galerkin Finite Element Methods for Second Order Elliptic Problems. Numerical Mathematics: Theory, Methods and Applications. 14 (3). 613-623. doi:10.4208/nmtma.OA-2020-0120
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