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

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.