Wavelet stabilization of the Lagrange multiplier method

Summary.

We propose here a stabilization strategy for the Lagrange multiplier formulation of Dirichlet problems. The stabilization is based on the use of equivalent scalar products for the spaces $H^{1/2}(\partial\Omega)$ and $H^{-1/2}(\partial\Omega)$, which are realized by means of wavelet functions. The resulting stabilized bilinear form is coercive with respect to the natural norm associated to the problem. A uniformly coercive approximation of the stabilized bilinear form is constructed for a wide class of approximation spaces, for which an optimal error estimate is provided. Finally, a formulation is presented which is obtained by eliminating the multiplier by static condensation. This formulation is closely related to the Nitsche's method for solving Dirichlet boundary value problems.