I gave the keynote talk Structure-preserving numerical methods for dispersive wave equations in the section S18: Numerical methods for differential equations at the GAMM Annual Meeting 2023 in Dresden (Germany) on Wednesday, 2023-05-31, 14:00 CEST.
Structure-preserving numerical methods for dispersive wave equations
The numerical simulation of tsunami propagation is often based on the classical shallow water equations. However, there are several regimes where the assumptions used to derive this model are not satisfied. In this case, higher-order effects need to be taken into account, leading to nonlinear dispersive wave equations. Several variants of such models exist and are used in practice. In this contribution, we concentrate on the development and analysis of structure-preserving numerical methods. In particular, we will consider invariants such as the total energy and study efficient numerical methods yielding qualitative and quantitative improvements compared to standard schemes.