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.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
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
-
Uniform convergence of a weak Galerkin method for singularly perturbed convection–diffusion problems
Zhang, Jin | Liu, XiaoweiMathematics and Computers in Simulation, Vol. 200 (2022), Iss. P.393
https://doi.org/10.1016/j.matcom.2022.04.023 [Citations: 7] -
Mixed Weak Galerkin Method for Heat Equation with Random Initial Condition
Zhou, Chenguang | Zou, Yongkui | Chai, Shimin | Zhang, FengshanMathematical Problems in Engineering, Vol. 2020 (2020), Iss. P.1
https://doi.org/10.1155/2020/8796345 [Citations: 2] -
Invariant region property of weak Galerkin method for semilinear parabolic equations
Qin, Mingze | Wang, Xiuli | Zhou, HuifangJournal of Computational and Applied Mathematics, Vol. 460 (2025), Iss. P.116412
https://doi.org/10.1016/j.cam.2024.116412 [Citations: 0] -
A robust weak Galerkin finite element method for two parameter singularly perturbed parabolic problems on nonuniform meshes
Singh, Jasbir | Kumar, Naresh | Jiwari, RamJournal of Computational Science, Vol. 77 (2024), Iss. P.102241
https://doi.org/10.1016/j.jocs.2024.102241 [Citations: 3]