Adaptive frame methods for elliptic operator equations: the steepest descent approach |
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Authors: | Dahlke Stephan; Raasch Thorsten; Werner Manuel; Fornasier Massimo; Stevenson Rob |
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Institution: |
FB 12 Mathematik und Informatik, Philipps-Universität Marburg, Hans-Meerwein Straße, Lahnberge, D-35032 Marburg, Germany
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Abstract: |
Massimo Fornasier¶
Dipartimento di Metodi e Modelli Matematici per le Scienze Applicate, Università "La Sapienza" in Roma, Via Antonio Scarpa, 16/B, I-00161 Roma, Italy
Rob Stevenson||
Department of Mathematics, Utrecht University, PO Box 80.010, NL-3508 TA Utrecht, The Netherlands
This paper is concerned with the development of adaptive numericalmethods for elliptic operator equations. We are particularlyinterested 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 optimalcomputational complexity. The scheme is based on adaptive steepestdescent iterations. We illustrate our findings by numericalresults for the computation of solutions of the Poisson equationwith limited Sobolev smoothness on intervals in 1D and L-shapeddomains in 2D. |
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Keywords: | operator equations multiscale methods adaptive algorithms sparse matrices Banach frames norm equivalences |
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