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 - <p style="text-align: justify;">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.</p>