Unified a Posteriori Error Estimator for Finite Element Methods for the Stokes Equations

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.