Anisotropic curl-free wavelet bases on the unit cube

Abstract

This paper deals with the construction of anisotropic curl-free wavelets on the cube [0, 1]3, which satisfies the specific boundary conditions. First, one constructs curl-free wavelets on the unit cube based on one dimensional wavelets on the interval [0, 1] with some boundary conditions. Then, the stability of the corresponding wavelets in curl-free space and the characterization of Sobolev spaces are studied. Finally, one gives a Helmholtz decomposition and the representation of curl and div operators in wavelet coordinates.