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Convergence of 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
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.
Keywords : hydrostatic reconstruction Saint Venant system with topography well-balanced scheme convergence entropy inequality kinetic function Mathematics
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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⟩

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