Residual-based a posteriori error estimation for hp-adaptive finite element methods for the Stokes equations

Abstract

AbstractWe derive a residual-based a posteriori error estimator for the conforminghp-Adaptive Finite Element Method (hp-AFEM) for the steady state Stokes problem describing the slow motion of an incompressible fluid. This error estimator is obtained by extending the idea of a posteriori error estimation for the classicalh-version of AFEM. We also establish the reliability and efficiency of the error estimator. The proofs are based on the well-known Clément-type interpolation operator introduced in [27] in the context of thehp-AFEM. Numerical experiments show the performance of an adaptivehp-FEM algorithm using the proposed a posteriori error estimator.