Numerische Mathematik

, Volume 101, Issue 3, pp 423–450 | Cite as

The Fourier Singular Complement Method for the Poisson problem. Part I: prismatic domains

  • P. Ciarlet Jr
  • B. Jung
  • S. Kaddouri
  • S. Labrunie
  • J. Zou
Article

Abstract

This is the first part of a threefold article, aimed at solving numerically the Poisson problem in three-dimensional prismatic or axisymmetric domains. In this first part, the Fourier Singular Complement Method is introduced and analysed, in prismatic domains. In the second part, the FSCM is studied in axisymmetric domains with conical vertices, whereas, in the third part, implementation issues, numerical tests and comparisons with other methods are carried out. The method is based on a Fourier expansion in the direction parallel to the reentrant edges of the domain, and on an improved variant of the Singular Complement Method in the 2D section perpendicular to those edges. Neither refinements near the reentrant edges of the domain nor cut-off functions are required in the computations to achieve an optimal convergence order in terms of the mesh size and the number of Fourier modes used.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • P. Ciarlet Jr
    • 1
  • B. Jung
    • 2
  • S. Kaddouri
    • 1
  • S. Labrunie
    • 3
  • J. Zou
    • 4
  1. 1.CNRS-ENSTA-INRIA UMR 2706 POEMS32, boulevard VictorFrance
  2. 2.Department of MathematicsChemnitz University of TechnologyChemnitzGermany
  3. 3.IECNUniversité Henri Poincaré Nancy I & INRIA (Projet CALVI)Vandœuvre-lés-Nancy cedexFrance
  4. 4.Department of MathematicsThe Chinese University of Hong KongHong KongChina

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