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An efficient space-time adaptive wavelet Galerkin method for time-periodic parabolic partial differential equations


Authors: Sebastian Kestler, Kristina Steih and Karsten Urban
Journal: Math. Comp. 85 (2016), 1309-1333
MSC (2010): Primary 35B10, 41A30, 41A63, 65N30, 65Y20
DOI: https://doi.org/10.1090/mcom/3009
Published electronically: August 14, 2015
MathSciNet review: 3454366
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Abstract: We introduce a multitree-based adaptive wavelet Galerkin algorithm for space-time discretized linear parabolic partial differential equations, focusing on time-periodic problems. It is shown that the method converges with the best possible rate in linear complexity and can be applied for a wide range of wavelet bases. We discuss the implementational challenges arising from the Petrov-Galerkin nature of the variational formulation and present numerical results for the heat and a convection-diffusion-reaction equation.


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Additional Information

Sebastian Kestler
Affiliation: Institute for Numerical Mathematics, University of Ulm, Helmholtzstrasse 20, D-89069 Ulm, Germany
Email: sebastian.kestler@gmail.com

Kristina Steih
Affiliation: Institute for Numerical Mathematics, University of Ulm, Helmholtzstrasse 20, D-89069 Ulm, Germany
Email: kristina.steih@uni-ulm.de

Karsten Urban
Affiliation: Institute for Numerical Mathematics, University of Ulm, Helmholtzstrasse 20, D-89069 Ulm, Germany
Email: karsten.urban@uni-ulm.de

DOI: https://doi.org/10.1090/mcom/3009
Keywords: Time-periodic problems, tensor product approximation, wavelets, adaptivity, optimal computational complexity
Received by editor(s): August 2, 2013
Received by editor(s) in revised form: October 28, 2014
Published electronically: August 14, 2015
Additional Notes: This work has partly been supported by the Deutsche Forschungsgemeinschaft within the Research Training Group (Graduiertenkolleg) GrK1100 Modellierung, Analyse und Simulation in der Wirtschaftsmathematik at Ulm University
Article copyright: © Copyright 2015 American Mathematical Society

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