The nonconforming virtual element method for the Darcy-Stokes problem

被引：13
|
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.
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收藏
页数：23
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