Anita Gjesteland (Univ. Waterloo): Linear and non-linear stability for various PDEs and their discretisations

Zoom Link:
https://uni-kassel.zoom.us/j/96217091997?pwd=RVRaVVBRclFJYU9jczNZSWF3SXI2QT09

Meeting ID: 962 1709 1997
Passcode: cauchy

Abstract:

Stability of initial-boundary-value problems and their discretisations is vastly studied in research. For linear problems, stability can ensure continuous dependence on data and uniqueness of the solution, while for non-linear problems, stability estimates can help single out physically relevant weak solutions and provide certain bounds on the solution. Once some kind of stability estimate is obtained at the continuous level, we aim to prove similar properties of the discretisation of the problem. The summation-by-parts (SBP) operators are widely used in research for this purpose. In this talk, I will present the stability notions used during the work of my PhD, give an introduction to the SBP operators and how they allow for simple stability proofs, and briefly talk about some current projects that touch upon the same topics.