A robust a posteriori error estimator for the Oseen problem

TL;DR

This paper introduces a residual-based a posteriori error estimator for the convection-dominated Oseen problem, demonstrating its robustness and extending it to Navier-Stokes equations with supporting numerical evidence.

Contribution

It proposes a new error estimator for the Oseen problem that remains robust in convection-dominated regimes and discusses its extension to Navier-Stokes equations.

Findings

The estimator accurately measures global error in the chosen norm.

Numerical studies confirm the robustness of the estimator in convection-dominated regimes.

The extension to Navier-Stokes equations is feasible and discussed.

Abstract

A residual-based a posteriori error estimator is proposed for the incompressible Oseen problem in the convection-dominated regime. The SUPG/PSPG/grad-div stabilized finite element method is used as discretization. The error estimator estimates the global error in a norm that is used in the a priori error analysis of the method. Based on several hypotheses concerning the error and interpolation errors, the robustness of the estimator in the convection-dominated regime is proved. Numerical studies support the analytic results. Finally, the extension of the a posteriori error estimator to the steady-state Navier--Stokes equations is discussed.