An error estimate for a fictitious domain formulation using volumic Lagrange multipliers of a Dirichlet problem

In this Note, we propose an approximation of the solution of an homogeneous Dirichlet problem by means of a fictitious domain method with Lagrange multipliers. The multipliers are defined on a part B of the complementary set of the original domain omega in the fictitious domain Omega. We use P-1 finite elements on a mesh built up on Omega, quite independent of omega. We prove an error estimate in h(1/2-epsilon) for all epsilon positive.