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Schwarz Preconditioning for High Order Simplicial Finite Elements

  • Joachim Schöberl
  • Jens M. Melenk
  • Clemens G. A. Pechstein
  • Sabine C. Zaglmayr
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 55)

Abstract

This paper analyzes two-level Schwarz methods for matrices arising from the p-version finite element method on triangular and tetrahedral meshes. The coarse level consists of the lowest order finite element space. On the fine level, we investigate several decompositions with large or small overlap leading to optimal or close to optimal condition numbers. The analysis is confirmed by numerical experiments for a model problem.

Keywords

Domain Decomposition Domain Decomposition Method Interpolation Operator Tetrahedral Mesh Coarse Space 
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Copyright information

© Springer 2007

Authors and Affiliations

  • Joachim Schöberl
    • 1
  • Jens M. Melenk
    • 2
  • Clemens G. A. Pechstein
    • 3
  • Sabine C. Zaglmayr
    • 1
  1. 1.Radon Institute for Computational and Applied Mathematics (RICAM)Austria
  2. 2.Department of MathematicsThe University of ReadingUK
  3. 3.Institute for Computational MathematicsJohannes Kepler UniversityLinzAustria

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