Séance Séminaire

Séminaire ACSIOM

Space-time discretization of parabolic PDEs.

A variational formulation is the basis for finite element discretizations of 2nd order elliptic problems. In a similar way, for parabolic evolution equations we start with a space-time variational formulation and propose stable Petrov--Galerkin discretizations and preconditioners. This allows for space-time parallel computation. The discretization is based on tensor product bases, allowing to reuse existing spatial finite element codes. The multilevel preconditioners are obtained from the mapping properties of the continuous parabolic operator. We discuss analytical and algorithmic aspects, and show numerical experiments illustrating parallelization in time.