A time-explicit weak Galerkin scheme for parabolic equations on polytopal partitions-Reference-Cited by-同舟云学术

A time-explicit weak Galerkin scheme for parabolic equations on polytopal partitions

Published:2022-05-24 Issue:0 Volume:0 Page:
ISSN:1570-2820
Container-title:Journal of Numerical Mathematics
language:en
Short-container-title:

Author:

Wang Junping¹,Ye Xiu²,Zhang Shangyou³

Affiliation:

1. Division of Mathematical Sciences, National Science Foundation, Alexandria , VA 22314 Virginia , USA

2. Department of Mathematics, University of Arkansas at Little Rock , Little Rock , AR 72204 , USA

3. Department of Mathematical Sciences, University of Delaware , Newark , DE 19716 , USA

Abstract

Abstract In this paper a time-explicit weak Galerkin finite element method is introduced and analyzed for parabolic equations. The main idea relies on the inclusion of a stabilization term in the temporal direction in addition to the usual static stabilization in the weak Galerkin framework. Both semi-discrete and fully-discrete schemes in time are presented, as well as their stability and error analysis. Numerical results are reported for this new explicit weak Galerkin finite element method.

Publisher

Walter de Gruyter GmbH

Subject

Computational Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/jnma-2021-0128/pdf

Reference42 articles.

1. A. Al-Twaeel, S. Hussian and X. Wang, A stabilizer free weak Galerkin finite element method for parabolic equation, J. Comput. Appl. Math., 392 (2021), 113373.

2. G. Chen, M. Feng, X. Xie, A robust WG finite element method for convection–diffusion–reaction equations, J. Comput. Appl. Math., 315 (2017), 107-125.

3. W. Chen, F. Wang and Y. Wang, Weak Galerkin method for the coupled Darcy–Stokes flow, IMA J. Numer. Anal., 36 (2016), 897-921.

4. M. Cui and S. Zhang, On the uniform convergence of the weak Galerkin finite element method for a singularly-perturbed biharmonic equation, J. Sci. Comput., 82 (2020), 5-15.

5. B. Deka and P. Roy, Weak galerkin finite element methods for parabolic interface problems with nonhomogeneous jump conditions, Numer. Funct. Anal. Optim., 40 (2019), 250-279.

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