Distributed Lagrange multipliers based on fictitious domain method for second order elliptic problems

In this article we further investigate the solution of linear second order elliptic boundary value problems by distributed Lagrange multipliers based fictitious domain methods. The following issues are addressed: (i) Derivation of the fictitious domain formulations. (ii) Finite element approximation. (iii) Iterative solution of the resulting finite dimensional problems (of the saddle-point type) by preconditioned conjugate gradient and Lanczos algorithms.