Convergence analysis of a space-time approximation to a two-dimensional system of shallow water equations

Abstract

A characteristic-Galerkin approximation of a new two-dimensional Shallow Water viscous parabolic model is presented and a semi-implicit-Lagrangian finite element scheme is used. A convergence result is proved and numerical experiments on academic tests are shown.

Keywords:

• Shallow water equation
• Semi-implicit-Lagrangian finite element scheme
• Space-time approximation

Acknowledgments

The author is grateful to his PhD Advisor, Prof. Fausto Saleri (MOX, Politecnico di Milano, Dipartimento di Matematica), Prof. Giovanni Russo (Università Statale degli Studi di Catania, Dipartimento di Matematica e Informatica), Prof. Beno

t Perthame (École Normale Supérieure – DMA, INRIA Rocquencourt), and Prof. Grigory Panasenko (Équipe d'Analyse Numérique de l'Université de Saint-Étienne) for all their precious suggestions.