Year: 2019
Author: Li Zhang, Minfu Feng, Jian Zhang
Advances in Applied Mathematics and Mechanics, Vol. 11 (2019), Iss. 4 : pp. 890–910
Abstract
In this paper, we modify the weak Galerkin method introduced in [15] for Stokes equations. The modified method uses the $\mathbb{P}_k/\mathbb{P}_{k-1}$ $(k\geq1)$ discontinuous finite element combination for velocity and pressure in the interior of elements. Especially, the numerical traces ${v}_{hb}$ which are defined in the interface of the elements belong to the space $C^0(\mathcal{E}_h)$, this change leads to less degree of freedom for the resultant linear system. The stability, priori error estimates and $L^2$ error estimates for velocity are proved in this paper. In addition, we prove that the modified method also yields globally divergence-free velocity approximations and has uniform error estimates with respect to the Reynolds number. Finally, numerical results illustrate the performance of the method, support the theoretical properties of the estimator and show the efficiency of the algorithm.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.OA-2018-0138
Advances in Applied Mathematics and Mechanics, Vol. 11 (2019), Iss. 4 : pp. 890–910
Published online: 2019-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 21
Keywords: Weak Galerkin Stokes equations globally divergence-free less degree of freedom uniform error estimates.
Author Details
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A novel approach of superconvergence analysis of the bilinear-constant scheme for time-dependent Stokes equations
Yang, Huaijun
Applied Numerical Mathematics, Vol. 173 (2022), Iss. P.180
https://doi.org/10.1016/j.apnum.2021.12.003 [Citations: 3]