On the Stability of the ILU — Method for Singular Perturbed Finite Element Problems

  • Stefan Sauter
Part of the Notes on Numerical Fluid Mechanics (NNFM) book series (NNFM, volume 29)


The ILU-method for solving systems of linear equations arising by discretizing partial differential equations via finite elements is known as a robust smoother in a multigrid procedure. The stability of the ILU—method is the fundamental property in the theoretical examination of this algorithm. The usual (sufficient) conditions to ensure stability are maximum angles conditions for the grid, which are easy to satisfy for model problems, but are quite unrealistic for irregular domains or anisotropic problems. In our paper we analyse an elliptic problem on a degenerate grid and prove, that the stability does not depend on the perturbation. Numerical tests will support the theoretical examination.


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Copyright information

© Friedr. Vieweg & Sohn Verlagsgesellschaft mbH, Braunschweig/Wiesbaden 1993

Authors and Affiliations

  • Stefan Sauter
    • 1
  1. 1.Institut für Informatik und praktische MathematikKielGermany

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