Numerical Analysis and Scientific Computing Seminar | Gunilla Kreiss, Stability and Accuracy for initial-boundary value problems, revisited

For Zoom Link please contact ddelreyfernandez@uwaterloo.ca 

Speaker

Gunilla Kreiss, Uppsala University Department of Information Technology Division of Scientific Computing

Title

Stability and Accuracy for initial-boundary value problems, revisited

Abstract

Stability and accuracy for a numerical method approximating an initial boundary value problem are inherently linked together. Stability means that perturbations have a bounded effect on the discrete solution, and is usually characterized by a precise estimate in terms of norms. Such an estimate can be directly used to quantify the accuracy of the method. A very convenient and common way to investigate stability, and hence accuracy, is to use the energy method. If this approach fails one may instead attempt to get results after Laplace transforming in time. Such analysis is usually more involved, but sharper results may follow. In this talk we will show examples where it is rewarding to consider the problem in the Laplace domain.