In this talk, we will present a fictitious domain finite element method called φ-FEM, well suited for
elliptic problems posed in a domain given by a level-set function without requiring a mesh fitting the
boundary. Unlike other recent fictitious domain-type methods (XFEM, Cut-FEM), our approach does
not need any non-standard numerical integration, neither on the cut mesh elements nor on the actual
boundary. We shall present the proofs of optimal convergence of our methods on the example of Poisson
equation using Lagrange finite elements of any order. We will also give numerical tests illustrating the
optimal convergence of our methods and discuss the conditioning of resulting linear systems and the
robustness with respect to the geometry. We highlight the flexibility and efficiency of our method on
elastic and dynamic problems. And more recently, we propose a φ-FEM formulation to solve particulate
flows and Stokes equations.