Weak Galerkin Method for Second-Order Elliptic Equations with Newton Boundary Condition

Weak Galerkin Method for Second-Order Elliptic Equations with Newton Boundary Condition

Year:    2023

Author:    Mingze Qin, Ruishu Wang, Qilong Zhai, Ran Zhang

Communications in Computational Physics, Vol. 33 (2023), Iss. 2 : pp. 568–595

Abstract

The weak Galerkin (WG) method is a nonconforming numerical method for solving partial differential equations. In this paper, we introduce the WG method for elliptic equations with Newton boundary condition in bounded domains. The Newton boundary condition is a nonlinear boundary condition arising from science and engineering applications. We prove the well-posedness of the WG scheme by the monotone operator theory and the embedding inequality of weak finite element functions. The error estimates are derived. Numerical experiments 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/cicp.OA-2022-0138

Communications in Computational Physics, Vol. 33 (2023), Iss. 2 : pp. 568–595

Published online:    2023-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    28

Keywords:    Weak Galerkin method Newton boundary condition monotone operator embedding theorem.

Author Details

Mingze Qin

Ruishu Wang

Qilong Zhai

Ran Zhang