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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

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 L2 for the flux and H1 for the scalar function. Also an optimal order error estimate in L2 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 Email

Ran Zhang Email

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