, Volume 69, Issue 4, pp 339–352 | Cite as

Problem Dependent Generalized Prewavelets

  • C. Pflaum


In this paper, we present a new approach to construct robust multilevel algorithms for elliptic differential equations. The multilevel algorithms consist of multiplicative subspace corrections in spaces spanned by problem dependent generalized prewavelets. These generalized prewavelets are constructed by a local orthogonalization of hierarchical basis functions with respect to a so-called local coarse-grid space. Numerical results show that the local orthogonalization leads to a smaller constant in strengthened Cauchy-Schwarz inequality than the original hierarchical basis functions. This holds also for several equations with discontinuous coefficients. Thus, the corresponding multilevel algorithm is a fast and robust iterative solver.

AMS Subject Classifications: 65N55, 65N30. 
Keywords: Multilevel methods, generalized prewavelets. 


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Copyright information

© Springer-Verlag Wien 2002

Authors and Affiliations

  • C. Pflaum
    • 1
  1. 1.Institut für Angewandte Mathematik und Statistik Universität Würzburg Am Hubland D-97074 Würzburg Germany e-mail: pflaum@mathematik.uni-wuerzburg.deDE

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