Fictitious domain method for Dirichlet problems using mixed finite elements

摘要

In this note, we propose an approximation of the solution of a Dirichlet problem by means of a fictitious domain method. The original problem is replaced by a saddle-point problem defined on the fictitious domain Ω. To discretize the continuous problem, we use Raviart Thomas mixed finite elements. We give an error estimate and we prove that the condition number of the linear system to solve is independent of the discretization parameter.