CAM Seminar

Speaker: Abner J. Salgado

Affiliation: UTK

Title: Compactness properties of DIRK schemes

Abstract:

In this, possibly series of, talk(s) I will start by reviewing some notions of stability for ODE solvers like algebraic and B-stability, and I will argue that these are not enough to assert stability and convergence of, say, IRK schemes when applied to the discretization of (degenerate) parabolic-like PDEs.

Instead, while focusing on the class of DIRK schemes, I will introduce a new stability notion that completely mimics the natural a priori estimates of these PDEs. Verifying this notion amounts to solving a small eigenvalue problem, with size equal to the number of stages. I will present some popular class of schemes that do and do not satisfy this notion of stability.

Finally, we will see this notion in action when applied to the simulation of the so-called diocotron stability.

This is based on joint work with Ignacio Tomas (Texas Tech)