Stabilized wavelet approximations of the Stokes problem

Abstract

We propose a new consistent, residual-based stabilization of the Stokes problem. The stabilizing term involves a pseudo-differential operator, defined via a wavelet expansion of the test pressures. This yields control on the full L 2 L^2 -norm of the resulting approximate pressure independently of any discretization parameter. The method is particularly well suited for being applied within an adaptive discretization strategy. We detail the realization of the stabilizing term through biorthogonal spline wavelets, and we provide some numerical results.