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Convergence of the kinetic hydrostatic reconstruction scheme for the Saint Venant system with topography
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.
Cited literature [29 references]
https://hal-upec-upem.archives-ouvertes.fr/hal-01515256
Contributor : François Bouchut Connect in order to contact the contributor
Submitted on : Friday, September 4, 2020 - 11:32:09 AM
Last modification on : Tuesday, October 19, 2021 - 4:07:48 PM
Contributor : François Bouchut Connect in order to contact the contributor
Submitted on : Friday, September 4, 2020 - 11:32:09 AM
Last modification on : Tuesday, October 19, 2021 - 4:07:48 PM
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kin-hydrost_conv.pdf
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