Residual-Based a posteriori error estimation for hp-adaptive finite element methods for the Stokes equations
It extends a posteriori error estimation from h-version to hp-version for Stokes problems, providing a tool for adaptive mesh refinement in computational fluid dynamics.
The paper derives a residual-based a posteriori error estimator for hp-adaptive finite element methods for the Stokes equations, proving its reliability and efficiency, and demonstrating performance through numerical experiments.
We derive a residual-based a posteriori error estimator for the conforming hp-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 classical $h$-version of AFEM. We also establish the reliability and efficiency of the error estimator. The proofs are based on the well-known Clement-type interpolation operator introduced in 2005 in the context of the hp-AFEM. Numerical experiments show the performance of an adaptive hp-FEM algorithm using the proposed a posteriori error estimator.