The nonconforming virtual element method for the Darcy-Stokes problem

被引：11
|
作者：
Zhao, Jikun [1 ]
Zhang, Bei [2 ]
Mao, Shipeng [3 ,4 ]
Chen, Shaochun [1 ]
机构：
[1] Zhengzhou Univ, Sch Math & Stat, Zhengzhou 450001, Peoples R China
[2] Henan Univ Technol, Coll Sci, Zhengzhou 450001, Peoples R China
[3] Chinese Acad Sci, Acad Math & Syst Sci, Univ Chinese Acad Sci, LSEC, Beijing 100190, Peoples R China
[4] Chinese Acad Sci, Acad Math & Syst Sci, Univ Chinese Acad Sci, Inst Computat Math, Beijing 100190, Peoples R China
来源：
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING | 2020年 / 370卷
基金：
中国国家自然科学基金;
关键词：
Nonconforming virtual element; Darcy-Stokes problem; Uniform convergence; Polygonal mesh;
D O I：
10.1016/j.cma.2020.113251
中图分类号：
T [工业技术];
学科分类号：
08 ;
摘要：
We present the nonconforming virtual element method for the Darcy-Stokes problem. By using a gradient projection operator and a special polynomial subspace orthogonal to the gradient of some polynomial space, we construct a H-1-nonconforming but H(div)-conforming virtual element that allows us to compute the L-2-projection. The optimal convergence is proved under the assumption of sufficient regularity, and the uniform convergence is also obtained for the lowest-order case. Besides, we establish a discrete exact sequence of de Rham complex related to the nonconforming virtual element. Finally, we carry out some numerical tests to make a comparison of the convergence between different nonconforming virtual elements and confirm the optimal and uniform convergence of the nonconforming virtual element. (C) 2020 Elsevier B.V. All rights reserved.
引用
收藏
页数：23
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