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Piecewise Linear (Pre-)wavelets on Non-uniform Meshes

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Book cover Multigrid Methods V

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 3))

Abstract

In this paper, an explicit construction of compactly supported prewavelets on linear finite element spaces is introduced on non-uniform meshes on polyhedron domains and on boundaries of such domains. The obtained basas are stable in the Sobolev spaces Hr for |r| < 3/2. The only condition we need is that of uniform refinements. Compared to existing prewavelets bases on uniform meshes, with our construction the basis transformation from wavelet- to nodal basis (the wavelet transform) can be implemented more efficiently.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Nijmegen University, P.O. Box 9010, NL-6500 GL, Nijmegen, The Netherlands

    Rob Stevenson

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  1. Rob Stevenson
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Editor information

Editors and Affiliations

  1. Mathematisches Seminar, Universität Kiel, Ohlhausenstraße 40, D-24098, Kiel, Germany

    Wolfgang Hackbusch

  2. Technische Simulation iWR: Interdisziplinäres Zentrum für Wissenschaftliches Rechnen, Universität Heidelberg, Im Neuenheimer Feld 368, D-69120, Heidelberg, Germany

    Gabriel Wittum

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© 1998 Springer-Verlag Berlin Heidelberg

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Stevenson, R. (1998). Piecewise Linear (Pre-)wavelets on Non-uniform Meshes. In: Hackbusch, W., Wittum, G. (eds) Multigrid Methods V. Lecture Notes in Computational Science and Engineering, vol 3. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-58734-4_18

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  • DOI: https://doi.org/10.1007/978-3-642-58734-4_18

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-63133-0

  • Online ISBN: 978-3-642-58734-4

  • eBook Packages: Springer Book Archive

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