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
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
- Information
- Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 130 , Issue 1 , February 2000 , pp. 107 - 140
- Copyright
- Copyright © Royal Society of Edinburgh 2000
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