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Volume 33, Issue 2
Weak Galerkin Method for Second-Order Elliptic Equations with Newton Boundary Condition

Mingze Qin, Ruishu Wang, Qilong Zhai & Ran Zhang

DOI: 10.4208/cicp.OA-2022-0138

Commun. Comput. Phys., 33 (2023), pp. 568-595.

Published online: 2023-03

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  • 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.

  • Keywords

Weak Galerkin method, Newton boundary condition, monotone operator, embedding theorem.

  • AMS Subject Headings

65N30, 65N15, 35J65

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CiCP-33-568, author = {Qin , MingzeWang , RuishuZhai , Qilong and Zhang , Ran}, title = {Weak Galerkin Method for Second-Order Elliptic Equations with Newton Boundary Condition}, journal = {Communications in Computational Physics}, year = {2023}, volume = {33}, number = {2}, pages = {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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2022-0138}, url = {http://global-sci.org/intro/article_detail/cicp/21500.html} }
TY - JOUR T1 - Weak Galerkin Method for Second-Order Elliptic Equations with Newton Boundary Condition AU - Qin , Mingze AU - Wang , Ruishu AU - Zhai , Qilong AU - Zhang , Ran JO - Communications in Computational Physics VL - 2 SP - 568 EP - 595 PY - 2023 DA - 2023/03 SN - 33 DO - http://doi.org/10.4208/cicp.OA-2022-0138 UR - https://global-sci.org/intro/article_detail/cicp/21500.html KW - Weak Galerkin method, Newton boundary condition, monotone operator, embedding theorem. AB -

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.

Mingze Qin, Ruishu Wang, Qilong Zhai & Ran Zhang. (2023). Weak Galerkin Method for Second-Order Elliptic Equations with Newton Boundary Condition. Communications in Computational Physics. 33 (2). 568-595. doi:10.4208/cicp.OA-2022-0138
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