Humboldt-Universität zu Berlin - Mathematisch-Naturwissenschaftliche Fakultät - Institut für Mathematik

Preprint 2013-09



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


Carsten Carstensen , Christian Merdon


MSC 2000

  • 65N30 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
  • 65N15 Error bounds


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 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 effectivity indices between 1 to 4.