Error estimators for nonconforming finite element approximations of the Stokes problem

1995/01/01 by Enzo Dari, Enzo A. Dari, Ricardo Durán +2 · 2 citations
Engineering · Physics and Astronomy · #Advanced Numerical Methods in Computational Mathematics #Electromagnetic Simulation and Numerical Methods #Model Reduction and Neural Networks

paper · pdf · doi:10.1090/s0025-5718-1995-1284666-9

Abstract

In this paper we define and analyze a posteriori error estimators for nonconforming approximations of the Stokes equations. We prove that these estimators are equivalent to an appropriate norm of the error. For the case of piecewise linear elements we define two estimators. Both of them are easy to compute, but the second is simpler because it can be computed using only the right-hand side and the approximate velocity. We show how the first estimator can be generalized to higher-order elements. Finally, we present several numerical examples in which one of our estimators is used for adaptive refinement.

Cited by

• A unifying theory of a posteriori finite element error control
• Optimal adaptive nonconforming FEM for the Stokes problem

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