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Journal Articles Journal of Computational and Applied Mathematics Year : 2013

Effective construction of divergence-free wavelets on the square

Abstract

We present an effective construction of divergence-free wavelets on the square, with suitable boundary conditions. Since 2D divergence-free vector functions are the curl of scalar stream-functions, we simply derive divergence-free multiresolution spaces and wavelets by considering the curl of standard biorthogonal multiresolution analyses (BMRAs) on the square. The key point of the theory is that the derivative of a 1D BMRA is also a BMRA, as established by Jouini and Lemari'e-Rieusset [11]. We propose such construction in the context of generic compactly supported wavelets, which allows fast algorithms. Examples illustrate the practicality of the method.
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Dates and versions

hal-00727038 , version 1 (31-08-2012)

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Souleymane Kadri Harouna, Valérie Perrier. Effective construction of divergence-free wavelets on the square. Journal of Computational and Applied Mathematics, 2013, 240, pp.74-86. ⟨10.1016/j.cam.2012.07.029⟩. ⟨hal-00727038⟩
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