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Volume 26, Issue 5
Convergence of a Mixed Finite Element for the Stokes Problem on Anisotropic Meshes

Qingshan Li, Huixia Sun & Shaochun Chen

J. Comp. Math., 26 (2008), pp. 740-755.

Published online: 2008-10

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  • Abstract

The main aim of this paper is to study the convergence properties of a low order mixed finite element for the Stokes problem under anisotropic meshes. We discuss the anisotropic convergence and superconvergence independent of the aspect ratio. Without the shape regularity assumption and inverse assumption on the meshes, the optimal error estimates and natural superconvergence at central points are obtained. The global superconvergence for the gradient of the velocity and the pressure is derived with the aid of a suitable postprocessing method. Furthermore, we develop a simple method to obtain the superclose properties which improves the results of the previous works.

  • Keywords

Mixed finite element, Stokes problem, Anisotropic meshes, Superconvergence, Shape regularity assumption and inverse assumption.

  • AMS Subject Headings

65N30.

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-26-740, author = {Qingshan Li, Huixia Sun and Shaochun Chen}, title = {Convergence of a Mixed Finite Element for the Stokes Problem on Anisotropic Meshes}, journal = {Journal of Computational Mathematics}, year = {2008}, volume = {26}, number = {5}, pages = {740--755}, abstract = {

The main aim of this paper is to study the convergence properties of a low order mixed finite element for the Stokes problem under anisotropic meshes. We discuss the anisotropic convergence and superconvergence independent of the aspect ratio. Without the shape regularity assumption and inverse assumption on the meshes, the optimal error estimates and natural superconvergence at central points are obtained. The global superconvergence for the gradient of the velocity and the pressure is derived with the aid of a suitable postprocessing method. Furthermore, we develop a simple method to obtain the superclose properties which improves the results of the previous works.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8656.html} }
TY - JOUR T1 - Convergence of a Mixed Finite Element for the Stokes Problem on Anisotropic Meshes AU - Qingshan Li, Huixia Sun & Shaochun Chen JO - Journal of Computational Mathematics VL - 5 SP - 740 EP - 755 PY - 2008 DA - 2008/10 SN - 26 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/8656.html KW - Mixed finite element, Stokes problem, Anisotropic meshes, Superconvergence, Shape regularity assumption and inverse assumption. AB -

The main aim of this paper is to study the convergence properties of a low order mixed finite element for the Stokes problem under anisotropic meshes. We discuss the anisotropic convergence and superconvergence independent of the aspect ratio. Without the shape regularity assumption and inverse assumption on the meshes, the optimal error estimates and natural superconvergence at central points are obtained. The global superconvergence for the gradient of the velocity and the pressure is derived with the aid of a suitable postprocessing method. Furthermore, we develop a simple method to obtain the superclose properties which improves the results of the previous works.

Qingshan Li, Huixia Sun and Shaochun Chen. (2008). Convergence of a Mixed Finite Element for the Stokes Problem on Anisotropic Meshes. Journal of Computational Mathematics. 26 (5). 740-755. doi:
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