Recovery-Based Error Estimator for Stabilized Finite Element Method for the Stationary Navier--Stokes Problem

Abstract

A recovery-based error estimator is proposed and analyzed for stabilized $P_1/P_0$ (continuous linear velocity/constant pressure) finite element approximations to the stationary Navier--Stokes problem. We establish the reliability and efficiency of the error estimator. A crucial part of this work is the estimation for the nonlinear term of the Navier--Stokes problem. It turns out such a term can be bounded by the recovery-based error estimator. Numerical results are provided to illustrate the performance of the error estimator.