Résumé
Thanks to a finite element method, we solve numerically parabolic partial
differential equations on complex domains by avoiding the mesh generation,
using a regular background mesh, not fitting the domain and its real boundary
exactly. Our technique follows the phi-FEM paradigm, which supposes that the
domain is given by a level-set function. In this paper, we prove a priori error
estimates in l2(H1) and linf(L2) norms for an implicit Euler discretization in
time. We give numerical illustrations to highlight the performances of phi-FEM,
which combines optimal convergence accuracy, easy implementation process and
fastness.