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.