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Volume 34, Issue 5
A Weak Galerkin Mixed Finite Element Method for Second-Order Elliptic Equations with Robin Boundary Conditions

Qian Zhang & Ran Zhang

DOI: 10.4208/jcm.1604-m2015-0413

J. Comp. Math., 34 (2016), pp. 532-548.

Published online: 2016-10

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  • 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.

  • Keywords

Second-order elliptic equations, Robin boundary conditions, Weak Galerkin, Weak divergence.

  • AMS Subject Headings

65N30, 65N15, 65N12, 74N20.

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

qianzhang@csrc.ac.cn (Qian Zhang)

zhangran@jlu.edu.cn (Ran Zhang)

  • BibTex
  • RIS
  • TXT
@Article{JCM-34-532, author = {Zhang , Qian and Zhang , Ran}, title = {A Weak Galerkin Mixed Finite Element Method for Second-Order Elliptic Equations with Robin Boundary Conditions}, journal = {Journal of Computational Mathematics}, year = {2016}, volume = {34}, number = {5}, pages = {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.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1604-m2015-0413}, url = {http://global-sci.org/intro/article_detail/jcm/9811.html} }
TY - JOUR T1 - A Weak Galerkin Mixed Finite Element Method for Second-Order Elliptic Equations with Robin Boundary Conditions AU - Zhang , Qian AU - Zhang , Ran JO - Journal of Computational Mathematics VL - 5 SP - 532 EP - 548 PY - 2016 DA - 2016/10 SN - 34 DO - http://doi.org/10.4208/jcm.1604-m2015-0413 UR - https://global-sci.org/intro/article_detail/jcm/9811.html KW - Second-order elliptic equations, Robin boundary conditions, Weak Galerkin, Weak divergence. AB -

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.

Qian Zhang & Ran Zhang. (2020). A Weak Galerkin Mixed Finite Element Method for Second-Order Elliptic Equations with Robin Boundary Conditions. Journal of Computational Mathematics. 34 (5). 532-548. doi:10.4208/jcm.1604-m2015-0413
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