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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

On interpolatory divergence-free wavelets


Authors: Kai Bittner and Karsten Urban
Journal: Math. Comp. 76 (2007), 903-929
MSC (2000): Primary 42C40, 35Q30, 41A15
Published electronically: December 28, 2006
MathSciNet review: 2291842
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Abstract: We construct interpolating divergence-free multiwavelets based on cubic Hermite splines. We give characterizations of the relevant function spaces and indicate their use for analyzing experimental data of incompressible flow fields. We also show that the standard interpolatory wavelets, based on the Deslauriers-Dubuc interpolatory scheme or on interpolatory splines, cannot be used to construct compactly supported divergence-free interpolatory wavelets.


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Additional Information

Kai Bittner
Affiliation: University of Ulm, Institute for Numerical Mathematics, Helmholtzstr. 18, D-89069 Ulm, Germany
Email: kai.bittner@uni-ulm.de

Karsten Urban
Affiliation: University of Ulm, Institute for Numerical Mathematics, Helmholtzstr. 18, D-89069 Ulm, Germany
Email: karsten.urban@uni-ulm.de

DOI: http://dx.doi.org/10.1090/S0025-5718-06-01949-1
PII: S 0025-5718(06)01949-1
Keywords: Interpolatory wavelets, divergence-free vector fields
Received by editor(s): March 18, 2005
Received by editor(s) in revised form: March 13, 2006
Published electronically: December 28, 2006
Additional Notes: We are grateful to Nicolas Kevlahan for bringing our attention to the topic of this paper.
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.