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Volume 27, Issue 2-3
Low Order Nonconforming Rectangular Finite Element Methods for Darcy-Stokes Problems

Shiquan Zhang, Xiaoping Xie & Yumei Chen

J. Comp. Math., 27 (2009), pp. 400-424.

Published online: 2009-04

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  • Abstract

In this paper, we consider lower order rectangular finite element methods for the singularly perturbed Stokes problem. The model problem reduces to a linear Stokes problem when the perturbation parameter is large and degenerates to a mixed formulation of Poisson's equation as the perturbation parameter tends to zero. We propose two 2D and two 3D nonconforming rectangular finite elements, and derive robust discretization error estimates. Numerical experiments are carried out to verify the theoretical results.

  • Keywords

Darcy-Stokes problem, Finite element, Uniformly stable.

  • AMS Subject Headings

65N12, 65N15, 65N22, 65N30.

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-27-400, author = {Shiquan Zhang, Xiaoping Xie and Yumei Chen}, title = {Low Order Nonconforming Rectangular Finite Element Methods for Darcy-Stokes Problems}, journal = {Journal of Computational Mathematics}, year = {2009}, volume = {27}, number = {2-3}, pages = {400--424}, abstract = {

In this paper, we consider lower order rectangular finite element methods for the singularly perturbed Stokes problem. The model problem reduces to a linear Stokes problem when the perturbation parameter is large and degenerates to a mixed formulation of Poisson's equation as the perturbation parameter tends to zero. We propose two 2D and two 3D nonconforming rectangular finite elements, and derive robust discretization error estimates. Numerical experiments are carried out to verify the theoretical results.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8579.html} }
TY - JOUR T1 - Low Order Nonconforming Rectangular Finite Element Methods for Darcy-Stokes Problems AU - Shiquan Zhang, Xiaoping Xie & Yumei Chen JO - Journal of Computational Mathematics VL - 2-3 SP - 400 EP - 424 PY - 2009 DA - 2009/04 SN - 27 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/8579.html KW - Darcy-Stokes problem, Finite element, Uniformly stable. AB -

In this paper, we consider lower order rectangular finite element methods for the singularly perturbed Stokes problem. The model problem reduces to a linear Stokes problem when the perturbation parameter is large and degenerates to a mixed formulation of Poisson's equation as the perturbation parameter tends to zero. We propose two 2D and two 3D nonconforming rectangular finite elements, and derive robust discretization error estimates. Numerical experiments are carried out to verify the theoretical results.

Shiquan Zhang, Xiaoping Xie and Yumei Chen. (2009). Low Order Nonconforming Rectangular Finite Element Methods for Darcy-Stokes Problems. Journal of Computational Mathematics. 27 (2-3). 400-424. doi:
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