Distributed Lagrange Multiplier Functions for Fictitious Domain Method with Spectral/hp Element Discretization

A fictitious domain approach for the solution of second-order linear differential problems is proposed; spectral/hp elements have been used for the discretization of the domain. The peculiarity of our approach is that the Lagrange multipliers are particular distributed functions, instead of classical δ Dirac (impulsive)multipliers. In this paper we present the formulation and the application of this approach to 1D and 2D Poisson problems and 2D Stokes flow (biharmonic equation).