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Author:

Liu, Xin (Liu, Xin.) | Li, Jian (Li, Jian.) | Chen, Zhangxin (Chen, Zhangxin.)

Indexed by:

SCIE EI Scopus

Abstract:

In this paper, a nonconforming virtual element method for the Stokes problem is proposed and investigated. This method gives a unified scheme for two and three dimensions simultaneously. In addition, it provides an attractive computational feature treatment of general elements including non-convex and degenerate elements. Moreover, by choosing a proper low order velocity and pressure pair, we prove the discrete inf-sup condition for this method to obtain its solvability and stability. Furthermore, we show optimal energy norm error estimates for velocity and L-2 norm error estimates for both velocity and pressure. Finally, a series of numerical experiments are performed to validate that this method has good stability and accuracy for the Stokes problem. (C) 2017 Elsevier B.V. All rights reserved.

Keyword:

General elements Inf-Sup condition Nonconforming virtual element method Optimal error estimates Stokes problem

Author Community:

  • [ 1 ] [Liu, Xin; Chen, Zhangxin] Xi An Jiao Tong Univ, Sch Math & Stat, Xian 710049, Peoples R China
  • [ 2 ] [Li, Jian] Shaanxi Univ Sci & Technol, Sch Arts & Sci, Xian 710021, Peoples R China
  • [ 3 ] [Li, Jian] Baoji Univ Arts & Sci, Dept Math, Baoji 721013, Peoples R China
  • [ 4 ] [Chen, Zhangxin] Univ Calgary, Schulich Sch Engn, Dept Chem & Petr Engn, 2500 Univ Dr NW, Calgary, AB T2N 1N4, Canada
  • [ 5 ] [Liu, Xin]Xi An Jiao Tong Univ, Sch Math & Stat, Xian 710049, Peoples R China
  • [ 6 ] [Chen, Zhangxin]Xi An Jiao Tong Univ, Sch Math & Stat, Xian 710049, Peoples R China
  • [ 7 ] [Li, Jian]Shaanxi Univ Sci & Technol, Sch Arts & Sci, Xian 710021, Peoples R China
  • [ 8 ] [Li, Jian]Baoji Univ Arts & Sci, Dept Math, Baoji 721013, Peoples R China
  • [ 9 ] [Chen, Zhangxin]Univ Calgary, Schulich Sch Engn, Dept Chem & Petr Engn, 2500 Univ Dr NW, Calgary, AB T2N 1N4, Canada

Reprint Author's Address:

  • Xi An Jiao Tong Univ, Sch Math & Stat, Xian 710049, Peoples R China.

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Source :

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING

ISSN: 0045-7825

Year: 2017

Volume: 320

Page: 694-711

4 . 4 4 1

JCR@2017

6 . 7 5 6

JCR@2020

ESI Discipline: COMPUTER SCIENCE;

ESI HC Threshold:135

JCR Journal Grade:2

CAS Journal Grade:1

Cited Count:

WoS CC Cited Count: 37

SCOPUS Cited Count: 62

ESI Highly Cited Papers on the List: 0 Unfold All

WanFang Cited Count:

Chinese Cited Count:

30 Days PV: 5

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