Low Regularity Error Analysis for Weak Galerkin Finite Element Methods for Second Order Elliptic Problems

Low Regularity Error Analysis for Weak Galerkin Finite Element Methods for Second Order Elliptic Problems

Year:    2021

Author:    Xiu Ye, Shangyou Zhang

Numerical Mathematics: Theory, Methods and Applications, Vol. 14 (2021), Iss. 3 : pp. 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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/nmtma.OA-2020-0120

Numerical Mathematics: Theory, Methods and Applications, Vol. 14 (2021), Iss. 3 : pp. 613–623

Published online:    2021-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    11

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

Author Details

Xiu Ye

Shangyou Zhang

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