The nonconforming virtual element method for the Navier-Stokes equations

被引：0
|
作者：
Xin Liu
Zhangxin Chen
机构：
[1] Xi’an Jiaotong University,School of Mathematics and Statistics
[2] Istituto di Matematica Applicata e Tecnologie Informatiche del C.N.R,College of Petroleum Engineering
[3] China University of Petroleum,Department of Chemical and Petroleum Engineering, Schulich School of Engineering
[4] University of Calgary,undefined
来源：
Advances in Computational Mathematics | 2019年 / 45卷
关键词：
Nonconforming virtual element method; Navier-Stokes equations; General elements; Stability; Energy and ; optimal error estimates; 65N30; 65N12; 65N15; 76D05;
D O I：
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中图分类号：
学科分类号：
摘要：
In this paper a unified nonconforming virtual element scheme for the Navier-Stokes equations with different dimensions and different polynomial degrees is described. Its key feature is the treatment of general elements including non-convex and degenerate elements. According to the properties of an enhanced nonconforming virtual element space, the stability of this scheme is proved based on the choice of a proper velocity and pressure pair. Furthermore, we establish optimal error estimates in the discrete energy norm for velocity and the L2 norm for both velocity and pressure. Finally, we test some numerical examples to validate the theoretical results.
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页码：51 / 74
页数：23
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