Rob Stevenson
Divergence-Free Wavelets on the Hypercube: General Boundary Conditions
Preprint series: ESI preprints

MSC:

42C15 Series of general orthogonal functions, generalized Fourier expansions, nonorthogonal expansions

65T20 Discrete and fast Fourier transforms

76D99 None of the above but in this section

Abstract: On the $n$-dimensional hypercube, for given $k\in \N_0$, biorthogonal wavelet
Riesz bases are constructed for the subspace of divergence free vector fields
of the Sobolev space $H^k((0,1)^n)^n$ with general homogeneous Dirichlet boundary
conditions, including slip or no-slip boundary conditions.
Both primal and dual wavelets can be constructed to be locally supported. The
construction of the isotropic wavelet bases is restricted to the square, but that
of the anisotropic wavelet bases applies to any space dimension $n$.


Keywords: Divergence free wavelets, biorthogonal wavelets, anisotropic wavelets