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Numerische Mathematik

, Volume 105, Issue 2, pp 217–247 | Cite as

Weighted Clément operator and application to the finite element discretization of the axisymmetric Stokes problem

  • Zakaria Belhachmi
  • Christine Bernardi
  • Simone Deparis
Article

Abstract

We consider the Stokes problem in an axisymmetric three-dimensional domain with data which are axisymmetric and have angular component equal to zero. We observe that the solution is also axisymmetric and the velocity has also zero angular component, hence the solution satisfies a system of equations in the meridian domain. The weak three-dimensional problem reduces to a two-dimensional one with weighted integrals. The latter is discretized by Taylor–Hood type finite elements. A weighted Clément operator is defined and approximation results are proved. This operator is then used to derive the discrete inf–sup condition and optimal a priori error estimates.

Mathematics Subject Classification

35N30 35Q30 46E35 6N10 76D07 

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Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  • Zakaria Belhachmi
    • 1
  • Christine Bernardi
    • 2
  • Simone Deparis
    • 3
  1. 1.LMAM, UMR 7122Univ. de Metz, ISGMPMetz Cedex 01France
  2. 2.Laboratoire Jacques-Louis LionsC.N.R.S. et Univ. Pierre et Marie Curie, B.C.Paris Cedex 05France
  3. 3.CMCS-IACS, EPFLLausanneSuisse

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