An effective implementation for Stokes Equation by the weak Galerkin finite element method

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:370

Article

Wang, Xiuli¹  Zou, Yongkui¹  Zhai, Qilong¹ 

[1] Jilin Univ, Dept Math, Changchun, Peoples R China

关键词: Stokes equation;    Weak Galerkin finite element;    Weak divergence;    Weak gradient;    Schur complement;   

DOI  :  10.1016/j.cam.2019.112586

来源: Elsevier

【 摘 要 】

In this paper we introduce and analyze the Schur complement technique to a weak Galerkin (WG for short) finite element method for solving Stokes equation. Due to the special structure of the weak functions, the main idea of Schur decomposition method is to express the interior velocity functions defined inside partition elements in terms of the velocity functions defined on the partition boundary and the pressure functions. This can largely reduce the degree of freedom of the derived discrete linear system. We investigate the well-posedness of the solution generated from Schur complement and its coincidence with the standard WG method. Finally, we exhibit some numerical experiments to illustrate the theoretical analysis. (C) 2019 Elsevier B.V. All rights reserved.

【 授权许可】

Free