Convergence of the the kinetic hydrostatic reconstruction scheme for the Saint Venant system with topography

François Bouchut (1) , Xavier Lhébrard (1)

1 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées

We prove the convergence of the hydrostatic reconstruction scheme with kinetic numerical flux for the Saint Venant system with Lipschitz continuous topography. We use a recently derived fully discrete sharp entropy inequality with dissipation, that enables us to establish an estimate in the inverse of the square root of the space increment ∆x of the L 2 norm of the gradient of approximate solutions. By Diperna's method we conclude the strong convergence towards bounded weak entropy solutions.

Mots clés: Saint Venant system with topography; well-balanced scheme; hydrostatic reconstruction; convergence; entropy inequality

Domaines: Analyse numérique [math.NA]; Equations aux dérivées partielles [math.AP]

François Bouchut, Xavier Lhébrard. Convergence of the the kinetic hydrostatic reconstruction scheme for the Saint Venant system with topography. 2017. ⟨hal-01515256v1⟩