Convergence of the kinetic hydrostatic reconstruction scheme for the Saint Venant system with topography

Bouchut, François; Lhébrard, Xavier

doi:10.1090/mcom/3600

Convergence of the kinetic hydrostatic reconstruction scheme for the Saint Venant system with topography
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by François Bouchut and Xavier Lhébrard;

Math. Comp. 90 (2021), 1119-1153

DOI: https://doi.org/10.1090/mcom/3600

Published electronically: December 28, 2020

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Abstract:

We prove the convergence of the hydrostatic reconstruction scheme with kinetic numerical flux for the Saint Venant system with continuous topography with locally integrable derivative. 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.

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