Numerical Analysis Seminar

Date: October 26, 2022

Time: 3:00PM - 4:00PM

Location: BLOC 302

Speaker: Jean-Luc Guermond, Texas A&M University

Title: Invariant-domain preserving high-order implicit explicit time stepping for nonlinear conservation equations

Abstract: I consider high-order discretizations of a Cauchy problem where the evolution operator comprises a hyperbolic part and a parabolic part with diffusion and stiff relaxation terms. Assuming that this problem admits non-trivial invariant domains, in the talk I will discuss approximation techniques in time that preserve these invariant domains. Before going into the details, I am going to give an overview of the literature on the topic. Emphasis will be put on explicit and explicit Runge Kutta techniques using Butcher's formalism. Then I am going to describe techniques that make every implicit-explicit time stepping scheme invariant-domain preserving and mass conservative. The proposed methodology is agnostic to the space discretization and allows to optimize the time step restrictions induced by the hyperbolic sub-step.