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 $\Delta x$ 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.
Return to personal page