Reliable a posteriori error control for nonconforming finite element approximation of Stokes flow

Dörfler, W.; Ainsworth, M.

doi:10.1090/S0025-5718-05-01743-6

Reliable a posteriori error control for nonconforming finite element approximation of Stokes flow
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by W. Dörfler and M. Ainsworth;

Math. Comp. 74 (2005), 1599-1619

DOI: https://doi.org/10.1090/S0025-5718-05-01743-6

Published electronically: January 3, 2005

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Abstract:

We derive computable a posteriori error estimates for the lowest order nonconforming Crouzeix–Raviart element applied to the approximation of incompressible Stokes flow. The estimator provides an explicit upper bound that is free of any unknown constants, provided that a reasonable lower bound for the inf-sup constant of the underlying problem is available. In addition, it is shown that the estimator provides an equivalent lower bound on the error up to a generic constant.

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