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Volume 10, Issue 3
Unified a Posteriori Error Estimator for Finite Element Methods for the Stokes Equations

J. Wang, Y. Wang & X. Ye

Int. J. Numer. Anal. Mod., 10 (2013), pp. 551-570.

Published online: 2013-10

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  • Abstract

This paper is concerned with residual type a posteriori error estimators for finite element methods for the Stokes equations. In particular, the authors established a unified approach for deriving and analyzing a posteriori error estimators for velocity-pressure based finite element formulations for the Stokes equations. A general a posteriori error estimator was presented with a unified mathematical analysis for the general finite element formulation that covers conforming, non-conforming, and discontinuous Galerkin methods as examples. The key behind the mathematical analysis is the use of a lifting operator from discontinuous finite element spaces to continuous ones for which all the terms involving jumps at interior edges disappear.

  • Keywords

A posteriori error estimate, finite element methods, Stokes equations.

  • AMS Subject Headings

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

  • Copyright

COPYRIGHT: © Global Science Press

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  • TXT
@Article{IJNAM-10-551, author = {J. Wang, Y. Wang and X. Ye}, title = {Unified a Posteriori Error Estimator for Finite Element Methods for the Stokes Equations}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2013}, volume = {10}, number = {3}, pages = {551--570}, abstract = {

This paper is concerned with residual type a posteriori error estimators for finite element methods for the Stokes equations. In particular, the authors established a unified approach for deriving and analyzing a posteriori error estimators for velocity-pressure based finite element formulations for the Stokes equations. A general a posteriori error estimator was presented with a unified mathematical analysis for the general finite element formulation that covers conforming, non-conforming, and discontinuous Galerkin methods as examples. The key behind the mathematical analysis is the use of a lifting operator from discontinuous finite element spaces to continuous ones for which all the terms involving jumps at interior edges disappear.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/582.html} }
TY - JOUR T1 - Unified a Posteriori Error Estimator for Finite Element Methods for the Stokes Equations AU - J. Wang, Y. Wang & X. Ye JO - International Journal of Numerical Analysis and Modeling VL - 3 SP - 551 EP - 570 PY - 2013 DA - 2013/10 SN - 10 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/582.html KW - A posteriori error estimate, finite element methods, Stokes equations. AB -

This paper is concerned with residual type a posteriori error estimators for finite element methods for the Stokes equations. In particular, the authors established a unified approach for deriving and analyzing a posteriori error estimators for velocity-pressure based finite element formulations for the Stokes equations. A general a posteriori error estimator was presented with a unified mathematical analysis for the general finite element formulation that covers conforming, non-conforming, and discontinuous Galerkin methods as examples. The key behind the mathematical analysis is the use of a lifting operator from discontinuous finite element spaces to continuous ones for which all the terms involving jumps at interior edges disappear.

J. Wang, Y. Wang and X. Ye. (2013). Unified a Posteriori Error Estimator for Finite Element Methods for the Stokes Equations. International Journal of Numerical Analysis and Modeling. 10 (3). 551-570. doi:
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