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

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 L2 norm is O(h2). Numerical experiments are presented to support our theoretical results.

• Keywords

Stokes problem, finite volume method, constrained nonconforming rotated $Q_1$ element.

65N08, 65N15, 65N30, 76D05

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@Article{AAMM-4-46, author = {Jing Qi , and Wanfu Tian , and Li , Yonghai}, 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 L2 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} }
TY - JOUR T1 - A Finite Volume Method Based on the Constrained Nonconforming Rotated Q1-Constant Element for the Stokes Problem AU - Jing Qi , AU - Wanfu Tian , AU - Li , Yonghai JO - Advances in Applied Mathematics and Mechanics VL - 1 SP - 46 EP - 71 PY - 2012 DA - 2012/04 SN - 4 DO - http://doi.org/10.4208/aamm.11-m1156 UR - https://global-sci.org/intro/article_detail/aamm/106.html KW - Stokes problem, finite volume method, constrained nonconforming rotated $Q_1$ element. AB -

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.

Jing Qi, Wanfu Tian & Yonghai Li. (1970). A Finite Volume Method Based on the Constrained Nonconforming Rotated Q1-Constant Element for the Stokes Problem. Advances in Applied Mathematics and Mechanics. 4 (1). 46-71. doi:10.4208/aamm.11-m1156
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