Abstract : 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.
https://hal-upec-upem.archives-ouvertes.fr/hal-01515256
Contributor : François Bouchut <>
Submitted on : Friday, September 4, 2020 - 11:32:09 AM Last modification on : Wednesday, September 16, 2020 - 3:14:31 AM
François Bouchut, Xavier Lhébrard. Convergence of the kinetic hydrostatic reconstruction scheme for the Saint Venant system with topography. Mathematics of Computation, American Mathematical Society, In press. ⟨hal-01515256v3⟩