A regularized shallow-water waves system with slip-wall boundary conditions: Theory and numerical analysis
- Dimitrios Mitsotakis, Senior Lecturer, School of Mathematics and Statistic Victoria University of Wellington, New Zealand
B1 L4 R4214
In this talk we present the derivation of a new Boussinesq-type system to describe the propagation of long waves of small amplitude in a basin with mildly varying bottom topography. We prove the existence and uniqueness of weak solutions for maximal times that do not depend on the amplitude of the waves. We then present the numerical solution of the new system using Galerkin finite element methods and prove the convergence of the semidiscrete solution to the exact solution. The system appears to describe well water waves even in benchmark experiments that involve also general bathymetries.
Overview
Abstract
In this talk we present the derivation of a new Boussinesq-type system to describe the propagation of long waves of small amplitude in a basin with mildly varying bottom topography. We prove the existence and uniqueness of weak solutions for maximal times that do not depend on the amplitude of the waves. We then present the numerical solution of the new system using Galerkin finite element methods and prove the convergence of the semidiscrete solution to the exact solution. The system appears to describe well water waves even in benchmark experiments that involve also general bathymetries.
Brief Biography
Dimitrios Mitsotakis is senior lecturer at Victoria University of Wellington, New Zealand. He worked in the past at the Universities Paris 11, University of Minnesota and University of California, Merced.