A variational perspective on Galerkin-type time discretizations

Galerkin-type time discretizations provide a robust and flexible tool for the numerical approximation of time-dependent problems. By formulating the temporal evolution in a variational setting, these methods are endowed with outstanding stability and approximation properties, as well as a more natural reproduction of key features of the continuous problem at the discrete level. This talk gives an overview of continuous and discontinuous Galerkin time discretizations for parabolic and hyperbolic problems, highlighting their interpretation as variational time integrators and their advantages over classical time-stepping schemes. We also discuss the main challenges in the stability analysis of these methods, and present a recent approach that closes several gaps in the literature.

Contatto:
paola.antonietti@polimi.it