A Multilevel Method for Discontinuous Galerkin Approximation of Three-dimensional Elliptic Problems

  • Johannes K. Kraus
  • Satyendra K. Tomar
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 60)

We construct optimal order multilevel preconditioners for interiorpenalty discontinuous Galerkin (DG) finite element discretizations of 3D elliptic boundary-value problems. A specific assembling process is proposed which allows us to characterize the hierarchical splitting locally. This is also the key for a local analysis of the angle between the resulting subspaces. Applying the corresponding two-level basis transformation recursively, a sequence of algebraic problems is generated. These discrete problems can be associated with coarse versions of DG approximations (of the solution to the original variational problem) on a hierarchy of geometrically nested meshes. The presented numerical results demonstrate the potential of this approach.


Elliptic Problem Discontinuous Galerkin Discontinuous Galerkin Method Multilevel Method Order Elliptic Problem 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Johannes K. Kraus
    • 1
  • Satyendra K. Tomar
    • 1
  1. 1.Johann Radon Institute for Computational and Applied MathematicsLinzAustria

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