A Preconditioned Conjugate Residual Algorithm for the Stokes Problem

  • R. Verfürth
Part of the Notes on Numerical Fluid Mechanics book series (NNFM, volume 11)


We present a preconditioned conjugate residual algorithm for a mixed finite element discretization of the Stokes problem
$$ - \Delta \underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}\to {u} + \nabla \rho = \underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}\to {f} {\text{ }}in{\text{ }}\Omega {\text{ }},\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}\to {u} = 0{\text{ on }}\partial \Omega {\text{ }}div{\text{ }}\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}\to {u} = 0{\text{ }}in{\text{ }}\Omega $$
in a plane polygonal domain Ω. The preconditioning relies on the idea of hierarchical basis functions for finite elements (cf.[7, 8]). The algorithm has a quasi optimal convergence rate of 1-0(|logh|).


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Copyright information

© Springer Fachmedien Wiesbaden 1985

Authors and Affiliations

  • R. Verfürth
    • 1
    • 2
  1. 1.INRIA Domaine de Voluceau — RocquencourtLE CHESNAY CedexFrance
  2. 2.Mathematisches InstitutRUBBochumW. - Germany

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