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An Adaptive Wavelet Galerkin Algorithm for one and two Dimensional Flame Computations

  • This paper is concerned with the development of a self-adaptive spatial descretization for PDEs using a wavelet basis. A Petrov-Galerkin method [LPT91] is used to reduce the determination of the unknown at the new time step to the computation of scalar products. These have to be discretized in an appropriate way. We investigate this point in detail and devise an algorithm that has linear operation count with respect to the number of unknowns. It is tested with spline wavelets and Meyer wavelets retaining the latter for their better localisation at finite precision. The algorithm is then applied to the one dimensional thermodiffusive equations. We show that the adaption strategy merits to be modified in order to take into account the particular and very strong nonlinearity of this problem. Finally, a supplementary Fourier discretization permits the computation of two dimensional flame fronts.

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Author:J. Fröhlich, K. Schneider
URN (permanent link):urn:nbn:de:hbz:386-kluedo-6995
Serie (Series number):Berichte der Arbeitsgruppe Technomathematik (AGTM Report) (92)
Document Type:Preprint
Language of publication:English
Year of Completion:1993
Year of Publication:1993
Publishing Institute:Technische Universität Kaiserslautern
Date of the Publication (Server):2000/10/17
Faculties / Organisational entities:Fachbereich Mathematik
DDC-Cassification:5 Naturwissenschaften und Mathematik / 510 Mathematik
Licence (German):Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011