Wavelet Stabilization of the Lagrange Multiplier Method

S. Bertoluzza

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 Sobolev spaces of fractional index, 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.

Numer. Math. 86 (2000), 1--28

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