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Edge behaviour of the solution of the Stokes problem with applications to the finite-element method

Published online by Cambridge University Press:  11 July 2007

J. M.-S. Lubuma
Affiliation:
Department of Mathematics, Mamelodi Campus, Vista University, Private Bag X1311, Silverton 0127, South Africa
S. Nicaise
Affiliation:
MACS – Institut des Sciences et Techniques de Valenciennes, Université de Valenciennes et du Hainaut Cambrésis, B.P. 311 Le Mont Houy, 59304 Valenciennes Cedex, France

Abstract

The Stokes problem on a domain with edge singularities is considered. The decomposition of the solution into a regular part and blocks of singular functions is established. This, together with the tangential regularity of the solution, leads to a global regularity result in suitable weighted Sobolev spaces, the properties of which are investigated. The global regularity is exploited to generate an optimally convergent semi-discrete mesh refinement mixed finite-element method. In the particular case of a prismatic domain, the Fourier finite-element method, which is a fully discrete scheme, is implemented.

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 2000

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