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• W2102968800 abstract "Some years ago, compactly supported divergence-free wavelets were constructed which also gave rise to a stable (biorthogonal) wavelet splitting of $mathbf {H}(mathrm {div};Omega )$. These bases have successfully been used both in the analysis and numerical treatment of the Stokes and Navier–Stokes equations. In this paper, we construct stable wavelet bases for the stream function spaces $mathbf {H}(mathbf {curl};Omega )$. Moreover, $mathbf {curl}$-free vector wavelets are constructed and analysed. The relationship between $mathbf {H}(mathrm {div};Omega )$ and $mathbf {H}(mathbf {curl};Omega )$ are expressed in terms of these wavelets. We obtain discrete (orthogonal) Hodge decompositions. Our construction works independently of the space dimension, but in terms of general assumptions on the underlying wavelet systems in $L^2(Omega )$ that are used as building blocks. We give concrete examples of such bases for tensor product and certain more general domains $Omega subset mathbb {R}^n$. As an application, we obtain wavelet multilevel preconditioners in $mathbf {H}(mathrm {div};Omega )$ and $mathbf {H}(mathbf {curl};Omega )$." @default.
• W2102968800 created "2016-06-24" @default.
• W2102968800 creator A5008601082 @default.
• W2102968800 date "2000-05-19" @default.
• W2102968800 modified "2023-09-24" @default.
• W2102968800 title "Wavelet bases in $mathbf{H}( mathrm{div})$ and $mathbf{H}(mathbf{curl})$" @default.
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• W2102968800 doi "https://doi.org/10.1090/s0025-5718-00-01245-x" @default.
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