Computational Survey on A Posteriori Error Estimators for the Crouzeix–Raviart Nonconforming Finite Element Method for the Stokes Problem

Abstract. This survey compares different strategies for guaranteed error control for the lowest-order nonconforming Crouzeix–Raviart finite element method for the Stokes equations. The upper error bound involves the minimal distance of the computed piecewise gradient D NC u CR $\operatorname{D}_{\textup {NC}}u_{\textup {CR}}$ to the gradients of Sobolev functions with exact boundary conditions. Several improved suggestions for the cheap computation of such test functions compete in five benchmark examples. This paper provides numerical evidence that guaranteed error control of the nonconforming FEM is indeed possible for the Stokes equations with overall efficiency indices between 1 to 4 in the asymptotic range.

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