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

Carsten Carstensen; Christian Merdon

doi:10.1515/cmam-2013-0021

Publicly Available Published by De Gruyter September 5, 2013

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

Carsten Carstensen and Christian Merdon

From the journal Computational Methods in Applied Mathematics

https://doi.org/10.1515/cmam-2013-0021

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 DNCuCR 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.

Keywords: Nonconforming Finite Element Method; Crouzeix–Raviart Finite Element Method; Adaptive Finite Element Method; A Posteriori Error Estimation

MSC: 65N30; 65N15

Published Online: 2013-09-05

Published in Print: 2014-01-01

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

Abstract.

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