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Optimal error Estimates for the Stokes and Navier–Stokesequations with slip–boundary condition

Published online by Cambridge University Press:  15 August 2002

Eberhard Bänsch  and
Klaus Deckelnick
Eberhard Bänsch
Affiliation:
Universität Bremen, Fachbereich 3, Zentrum für Technomathematik, Postfach 330 440, 28334 Bremen, Germany. baensch@math.uni-bremen.de.
Klaus Deckelnick
Affiliation:
Centre for Mathematical Analysis and its Applications, School of Mathematical Sciences, University of Sussex, Falmer, Brighton BN1 9QH, England. k.p.deckelnick@sussex.ac.uk.
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Abstract

We consider a finite element discretization by the Taylor–Hood element for the stationary Stokes and Navier–Stokes equations with slip boundary condition. The slip boundary condition is enforced pointwise for nodal values of the velocity in boundary nodes. We prove optimal error estimates in the H1 and L2 norms for the velocity and pressure respectively.

Keywords

Stokes equationsNavier–Stokes equationsfinite elementsslip boundary conditionerror estimates.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 33 , Issue 5 , September 1999 , pp. 923 - 938
Copyright
© EDP Sciences, SMAI, 1999

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