Analysis of the MAC scheme for the three dimensional Stokes problem

被引：5
|
作者：
Xu, Minqiang [1 ]
Liu, Kai [2 ]
Zhang, Lei [1 ]
机构：
[1] Zhejiang Univ Technol, Coll Sci, Hangzhou 310023, Peoples R China
[2] East China Univ Technol, Sch Sci, Nanchang 330013, Jiangxi, Peoples R China
来源：
APPLIED NUMERICAL MATHEMATICS | 2023年 / 193卷
基金：
中国国家自然科学基金;
关键词：
MAC; FVEM; 3D-Stokes equations; Superconvergence; Optimal error estimate; FINITE-ELEMENT-METHOD; EQUATIONS; SUPERCONVERGENCE; CONVERGENCE;
D O I：
10.1016/j.apnum.2023.07.021
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we propose a marker and cell method (MAC) with a proper quadrature scheme over non-uniform cuboid grids by using a staggered finite volume element method (FVEM) for 3D Stokes equations. The stability of the proposed MAC scheme is proven under Petrov-Galerkin method. By establishing a connection between MAC and FVEM, we rigorously prove the superconvergence property and the optimal order L2 error estimate. Finally, numerical results verify our theoretical findings.& COPY; 2023 IMACS. Published by Elsevier B.V. All rights reserved.
引用
收藏
页码：131 / 147
页数：17
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