A Weak Galerkin Mixed Finite Element Method for Second-Order Elliptic Equations with Robin Boundary Conditions
Year: 2016
Author: Qian Zhang, Ran Zhang
Journal of Computational Mathematics, Vol. 34 (2016), Iss. 5 : pp. 532–548
Abstract
In this paper, we present a weak Galerkin (WG) mixed finite element method for solving the second-order elliptic equations with Robin boundary conditions. Stability and a priori error estimates for the coupled method are derived. We present the optimal order error estimate for the WG-MFEM approximations in a norm that is related to the $L^2$ for the flux and $H^1$ for the scalar function. Also an optimal order error estimate in $L^2$ is derived for the scalar approximation by using a duality argument. A series of numerical experiments is presented that verify our theoretical results.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.1604-m2015-0413
Journal of Computational Mathematics, Vol. 34 (2016), Iss. 5 : pp. 532–548
Published online: 2016-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 17
Keywords: Second-order elliptic equations Robin boundary conditions Weak Galerkin Weak divergence.