Séance Séminaire

Séminaire des Doctorant·e·s

A new unfitted finite element method: phi-FEM

Phi-FEM is a new finite element method, proposed to solve partial differential equations on complex domains, using simple non conform meshes. The method relies on the use of a level-set function phi, which defines the domain and its boundary. In this presentation, I will introduce the method in the simple case of the resolution of the Poisson equation with Dirichlet boundary conditions. Then I will present the extension of the method to the case of time-dependent PDE's, and more precisely the case of the Heat equation with Dirichlet boundary conditions. Then, I will present a way to combine phi-FEM and neural networks. I will illustrate the efficiency of this method using numerical results.