Killian Vuillemot (Université de Montpellier) A new unfitted finite element method: φ-FEM

mercredi 25 mars 2026, 10:30 → 11:30 Europe/Paris

Abstract: φ-FEM is a new finite element method, proposed to solve partial differential equations on complex domains, using simple non-conforming meshes. The method relies on the use of a level-set function φ, 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 to the case of mixed Dirichlet/Neumann boundary conditions. I will also present results for the resolution of the Heat equation with Dirichlet boundary conditions or linear and non-linear elasticity problems. I will finally present different evolutions of the method, including its combination with Neural Operators or the use of the finite difference method. I will also discuss perspectives and future challenges for φ-FEM.