Wavelet stabilization of the Lagrange multiplier method

We propose hers a stabilization strategy for the Lagrange multiplier formul ation of Dirichlet problems. The stabilization is based on the use of equiv alent scalar products for the spaces H-1/2(partial derivative Omega) and H- 1/2(partial derivative Omega), which are realized by means of wavelet funct ions. The resulting stabilized bilinear form is coercive with respect to th e natural norm associated to the problem. A uniformly coercive approximatio n of the stabilized bilinear form is constructed for a wide class of approx imation spaces, for which an optimal error estimate is provided. Finally, a formulation is presented which is obtained by eliminating the multiplier b y static condensation. This formulation is closely related to the Nitsche's method for solving Dirichlet boundary value problems. Mathematics Subject Classification (1991): 65N30.