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Finite Element Methods with Patches and Applications

  • Roland Glowinski
  • Jiwen He
  • Alexei Lozinski
  • Marco Picasso
  • Jacques Rappaz
  • Vittoria Rezzonico
  • Joël Wagner
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 55)

Abstract

We present a new method [7] for numerically solving elliptic problems with multi-scale data using multiple levels of not necessarily nested grids. We use a relaxation method that consists of calculating successive corrections to the solution in patches of finite elements. We analyse the spectral properties of the iteration operator [6]. We show how to evaluate the best relaxation parameter and what is the influence of patches size on the convergence of the method. Several numerical results in 2D and 3D are presented.

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Copyright information

© Springer 2007

Authors and Affiliations

  • Roland Glowinski
    • 1
  • Jiwen He
    • 1
  • Alexei Lozinski
    • 2
  • Marco Picasso
    • 2
  • Jacques Rappaz
    • 2
  • Vittoria Rezzonico
    • 2
  • Joël Wagner
    • 2
  1. 1.Department of MathematicsUniversity of HoustonHoustonUSA
  2. 2.Ecole Polytechnique Fédérale de LausanneInstitute of Analysis and Scientific ComputingSwitzerland

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