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Volume 9, Issue 1
A Posteriori Error Estimate for Stabilized Finite Element Methods for the Stokes Equations

J. Wang, Y. Wang & X. Ye

Int. J. Numer. Anal. Mod., 9 (2012), pp. 1-16.

Published online: 2012-09

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  • Abstract

Computation with adaptive grid refinement has proved to be a useful and efficient tool in scientific computing over the last several decades. The key behind this technique is the design of a good a posterior error estimator that provides a guidance on how and where grids should be refined. In this paper, the authors propose and analyze a posteriori error estimator for a stabilized finite element method in computational fluid dynamics. The main contributions of the paper are: (1) an efficient a posteriori error estimator is designed and analyzed for a general stabilized finite element method, (2) a rigorous mathematical analysis is established for a theoretical justification of its efficiency and generality to other applications, and (3) some computational results with a comparison with other methods are presented for a computational justification of the proposed a posteriori error estimator.

  • Keywords

A posteriori error estimate, finite element methods, CFD, adaptive grid refinement.

  • AMS Subject Headings

Primary 65N15, 65N30, 76D07, Secondary 35B45, 35J50

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-9-1, author = {J. Wang, Y. Wang and X. Ye}, title = {A Posteriori Error Estimate for Stabilized Finite Element Methods for the Stokes Equations}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2012}, volume = {9}, number = {1}, pages = {1--16}, abstract = {

Computation with adaptive grid refinement has proved to be a useful and efficient tool in scientific computing over the last several decades. The key behind this technique is the design of a good a posterior error estimator that provides a guidance on how and where grids should be refined. In this paper, the authors propose and analyze a posteriori error estimator for a stabilized finite element method in computational fluid dynamics. The main contributions of the paper are: (1) an efficient a posteriori error estimator is designed and analyzed for a general stabilized finite element method, (2) a rigorous mathematical analysis is established for a theoretical justification of its efficiency and generality to other applications, and (3) some computational results with a comparison with other methods are presented for a computational justification of the proposed a posteriori error estimator.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/607.html} }
TY - JOUR T1 - A Posteriori Error Estimate for Stabilized Finite Element Methods for the Stokes Equations AU - J. Wang, Y. Wang & X. Ye JO - International Journal of Numerical Analysis and Modeling VL - 1 SP - 1 EP - 16 PY - 2012 DA - 2012/09 SN - 9 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/607.html KW - A posteriori error estimate, finite element methods, CFD, adaptive grid refinement. AB -

Computation with adaptive grid refinement has proved to be a useful and efficient tool in scientific computing over the last several decades. The key behind this technique is the design of a good a posterior error estimator that provides a guidance on how and where grids should be refined. In this paper, the authors propose and analyze a posteriori error estimator for a stabilized finite element method in computational fluid dynamics. The main contributions of the paper are: (1) an efficient a posteriori error estimator is designed and analyzed for a general stabilized finite element method, (2) a rigorous mathematical analysis is established for a theoretical justification of its efficiency and generality to other applications, and (3) some computational results with a comparison with other methods are presented for a computational justification of the proposed a posteriori error estimator.

J. Wang, Y. Wang and X. Ye. (2012). A Posteriori Error Estimate for Stabilized Finite Element Methods for the Stokes Equations. International Journal of Numerical Analysis and Modeling. 9 (1). 1-16. doi:
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