Volume 4, Issue 1
A Finite Volume Method Based on the Constrained Nonconforming Rotated Q1-Constant Element for the Stokes Problem

Jing Qi, Wanfu Tian & Yonghai Li

Adv. Appl. Math. Mech., 4 (2012), pp. 46-71.

Published online: 2012-04

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  • 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 L 2 norm is O(h2). Numerical experiments are presented to support our theoretical results.

  • Keywords

Stokes problem finite volume method constrained nonconforming rotated Q1 element

  • AMS Subject Headings

65N08 65N15 65N30 76D05

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COPYRIGHT: © Global Science Press

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@Article{AAMM-4-46, author = {Jing Qi, Wanfu Tian and Yonghai Li}, title = {A Finite Volume Method Based on the Constrained Nonconforming Rotated Q1-Constant Element for the Stokes Problem}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2012}, volume = {4}, number = {1}, pages = {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 L 2 norm is O(h2). Numerical experiments are presented to support our theoretical results.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.11-m1156}, url = {http://global-sci.org/intro/article_detail/aamm/106.html} }
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