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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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Space-time adaptive wavelet methods for parabolic evolution problems
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by Christoph Schwab and Rob Stevenson PDF
Math. Comp. 78 (2009), 1293-1318 Request permission

Abstract:

With respect to space-time tensor-product wavelet bases, parabolic initial boundary value problems are equivalently formulated as bi-infinite matrix problems. Adaptive wavelet methods are shown to yield sequences of approximate solutions which converge at the optimal rate. In case the spatial domain is of product type, the use of spatial tensor product wavelet bases is proved to overcome the so-called curse of dimensionality, i.e., the reduction of the convergence rate with increasing spatial dimension.
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Additional Information
  • Christoph Schwab
  • Affiliation: Department of Mathematics, ETH Zürich, ETH Zentrum, HG G58.1, CH 8092 Zürich, Switzerland
  • MR Author ID: 305221
  • Email: schwab@math.ethz.ch
  • Rob Stevenson
  • Affiliation: Korteweg-de Vries Institute for Mathematics, Plantage Muidergracht 24, 1018 TV Amsterdam, The Netherlands
  • MR Author ID: 310898
  • Email: R.P.Stevenson.uva.nl
  • Received by editor(s): January 3, 2008
  • Received by editor(s) in revised form: July 23, 2008
  • Published electronically: November 25, 2008
  • © Copyright 2008 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Math. Comp. 78 (2009), 1293-1318
  • MSC (2000): Primary 35K10, 41A25, 46B28, 65N99, 65T60
  • DOI: https://doi.org/10.1090/S0025-5718-08-02205-9
  • MathSciNet review: 2501051