Weak Galerkin Method for Second-Order Elliptic Equations with Newton Boundary Condition (Communications in Computational Physics, 2023)
The weak Galerkin (WG) method is a nonconforming numerical method forsolving partial differential equations. In this paper, we introduce the WG method forelliptic equations with Newton boundary condition in bounded domains. The Newtonboundary 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 thetheoretical analysis.
Keywords: Weak Galerkin method; Newton boundary condition; monotone operator; embedding theorem.