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A Weak Galerkin Mixed Finite Element Method for Second-Order Elliptic Equations with Robin Boundary Conditions

A Weak Galerkin Mixed Finite Element Method for Second-Order Elliptic Equations with Robin Boundary Conditions
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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.

Author Details

Qian Zhang

Ran Zhang

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