The nonconforming virtual element method for the Navier-Stokes equations

被引：53
|
作者：
Liu, Xin [1 ,2 ]
Chen, Zhangxin [1 ,3 ,4 ]
机构：
[1] Xi An Jiao Tong Univ, Sch Math & Stat, Xian 710049, Shaanxi, Peoples R China
[2] CNR, Ist Matemat Appl & Tecnol Informat, Via Ferrata 5a, I-27100 Pavia, Italy
[3] China Univ Petr, Coll Petr Engn, Beijing, Peoples R China
[4] Univ Calgary, Dept Chem & Petr Engn, Schulich Sch Engn, 2500 Univ Dr NW, Calgary, AB T2N 1N4, Canada
来源：
ADVANCES IN COMPUTATIONAL MATHEMATICS | 2019年 / 45卷 / 01期
关键词：
Nonconforming virtual element method; Navier-Stokes equations; General elements; Stability; Energy and L-2 optimal error estimates; FINITE-DIFFERENCE METHOD; HIGHER-ORDER; CONVERGENCE ANALYSIS; DIFFUSION-PROBLEMS; STATIONARY STOKES;
D O I：
10.1007/s10444-018-9602-z
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
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 L-2 norm for both velocity and pressure. Finally, we test some numerical examples to validate the theoretical results.
引用
收藏
页码：51 / 74
页数：24
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