Adaptive frame methods for elliptic operator equations: The steepest descent approach

Stephan Dahlke, Thorsten Raasch, Manuel Werner, Massimo Fornasier, Rob Stevenson

Research output: Contribution to journalArticlepeer-review

41 Scopus citations

Abstract

This paper is concerned with the development of adaptive numerical methods for elliptic operator equations. We are particularly interested in discretization schemes based on wavelet frames. We show that by using three basic subroutines an implementable, convergent scheme can be derived, which, moreover, has optimal computational complexity. The scheme is based on adaptive steepest descent iterations. We illustrate our findings by numerical results for the computation of solutions of the Poisson equation with limited Sobolev smoothness on intervals in 1D and L-shaped domains in 2D. The author 2007. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.2007

Original languageEnglish
Pages (from-to)717-740
Number of pages24
JournalIMA Journal of Numerical Analysis
Volume27
Issue number4
DOIs
StatePublished - Oct 2007
Externally publishedYes

Keywords

  • Adaptive algorithms
  • Banach frames
  • Multiscale methods
  • Norm equivalences
  • Operator equations
  • Sparse matrices

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