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A Finite Volume Method Based on the Constrained Nonconforming Rotated Q<sub>1</sub>-Constant Element for the Stokes Problem

A Finite Volume Method Based on the Constrained Nonconforming Rotated Q<sub>1</sub>-Constant Element for the Stokes Problem

Year:    2012

Author:    Jing Qi, Wanfu Tian, Yonghai Li

Advances in Applied Mathematics and Mechanics, Vol. 4 (2012), Iss. 1 : pp. 46–71

Abstract

We construct a finite volume element method based on the constrained nonconforming rotated Q1-constant element (CNRQ1-P0) for the Stokes problem. Two meshes are needed, which are the primal mesh and the dual mesh. We approximate the velocity by CNRQ1 elements and the pressure by piecewise constants. The errors for the velocity in the H1 norm and for the pressure in the L2 norm are O(h) and the error for the velocity in the L2 norm is O(h2). Numerical experiments are presented to support our theoretical results.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/aamm.11-m1156

Advances in Applied Mathematics and Mechanics, Vol. 4 (2012), Iss. 1 : pp. 46–71

Published online:    2012-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    26

Keywords:    Stokes problem finite volume method constrained nonconforming rotated Q1 element.

Author Details

Jing Qi Email

Wanfu Tian Email

Yonghai Li Email