Orthonormal Wavelet Bases Adapted for Partial Differential Equations

with Boundary Conditions

Pascal Monasse and Valérie Perrier

We adapt ideas presented by Auscher to impose boundary conditions on the construction of multiresolution analyses on the interval, as introduced by Cohen, Daubechies and Vial. We construct new orthonormal wavelet bases on the interval satisfying homogeneous boundary conditions. This construction can be extanded to wavelet packets, in the case of one boundary condition at each edge.We present in detail the numerical computation of the filters and of
the derivative operators associated to these bases. We derive quadrature formulae in order to study the approximation error at the edge of the interval. Several examples illustrate the present construction.

SIAM J. on Math. Analysis (29)4, pp 1040-1065 (1998)
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