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.
Publié le : 2017-04-27
Classification:
convergence,
well-balanced scheme,
hydrostatic reconstruction,
Saint Venant system with topography,
entropy inequality,
MSC: 65M12, 76M12, 35L65,
[MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA],
[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP]
@article{hal-01515256,
author = {Bouchut, Fran\c cois and Lh\'ebrard, Xavier},
title = {Convergence of the the kinetic hydrostatic reconstruction scheme for the Saint Venant system with topography},
journal = {HAL},
volume = {2017},
number = {0},
year = {2017},
language = {en},
url = {http://dml.mathdoc.fr/item/hal-01515256}
}
Bouchut, François; Lhébrard, Xavier. Convergence of the the kinetic hydrostatic reconstruction scheme for the Saint Venant system with topography. HAL, Tome 2017 (2017) no. 0, . http://gdmltest.u-ga.fr/item/hal-01515256/