Construction of Globally Continuous Biorthogonal Wavelet Bases
on Domains in R2
Helmut Harbrecht
Fakultät f\"ur Mathematik,
Technische Universität Chemnitz, Germany
Abstract
In order to solve partial differential equations or boundary integral
equations with a conforming Wavelet-Galerkin-Scheme, globally continuous
biorthogonal wavelet bases are required with the following properties
- norm equivalences in a certain range of Sobolev spaces,
- vanishing moments,
- approximation order,
- boundary value conditions.
In this talk we present a construction that utilizes a domain decomposition
strategy. A biorthogonal wavelet system is construcuted where the
biorthogonality is given with respect to a modified scalar product. These
basis functions are shown satisfy the properties mentioned above.