A Posteriori Error Estimator for Weak Galerkin Finite Element Method for Stokes Problem Using Diagonalization Techniques

Zhang, Jiachuan2; Zhang, Ran1; Li, Jingzhi3,4

2022-12-01

10.1515/cmam-2022-0087

Computational Methods in Applied Mathematics   Impact Factor & Quartile

1609-4840

1609-9389

Based on a hierarchical basis a posteriori error estimator, an adaptive weak Galerkin finite element method (WGFEM) is proposed for the Stokes problem in two and three dimensions. In this paper, we propose two novel diagonalization techniques for velocity and pressure, respectively. Using diagonalization techniques, we need only to solve two diagonal linear algebraic systems corresponding to the degree of freedom to get the error estimator. The upper bound and lower bound of the error estimator are also shown to address the reliability of the adaptive method. Numerical simulations are provided to demonstrate the effectiveness and robustness of our algorithm.

Diagonalization Techniques Weak Galerkin Hierarchical Basis A Posteriori Error Estimate Stokes Problem

SCI

English

Others

[BK20210540] ; [21KJB110015] ; [2020YFA0713601] ; [11971221] ; [2021ZDZX1001] ; [RCJC20200714114556020] ; [JCYJ20200109115422828] ; [JCYJ20190809150413261]

Mathematics

Mathematics, Applied

WOS:000894405900001

WALTER DE GRUYTER GMBH

Web of Science

1.Jilin Univ, Sch Math, Changchun 130012, Jilin, Peoples R China
2.Nanjing Tech Univ, Sch Phys & Math Sci, Nanjing 211816, Peoples R China
3.Southern Univ Sci & Technol, Dept Math, Shenzhen 518055, Peoples R China
4.Southern Univ Sci & Technol, Natl Ctr Appl Math, Shenzhen & SUSTech Int Ctr Math, Shenzhen 518055, Peoples R China

Zhang, Jiachuan,Zhang, Ran,Li, Jingzhi. A Posteriori Error Estimator for Weak Galerkin Finite Element Method for Stokes Problem Using Diagonalization Techniques[J]. Computational Methods in Applied Mathematics,2022.

Zhang, Jiachuan,Zhang, Ran,&Li, Jingzhi.(2022).A Posteriori Error Estimator for Weak Galerkin Finite Element Method for Stokes Problem Using Diagonalization Techniques.Computational Methods in Applied Mathematics.

Zhang, Jiachuan,et al."A Posteriori Error Estimator for Weak Galerkin Finite Element Method for Stokes Problem Using Diagonalization Techniques".Computational Methods in Applied Mathematics (2022).