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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} }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.