Applications

In this chapter, we describe some applications of the wavelet bases described above. These applications are of two types. First, we use the strong analytical properties combined with the particular construction of wavelets in H(div; Ω) and H(curl; Ω) in order to prove robustness and optimality of wavelet preconditioners in a Wavelet-Galerkin method for certain relevant problems. These problems include the Lamé equations in linear elasticity, Maxwell’s equations in electromagnetism and formulations of the incompressible Navier-Stokes equations in the primitive variables.