Transient L1 error estimates for well-balanced schemes on non-resonant scalar balance laws, J. Diff. Eq, vol.255, pp.469-502, 2013. ,
URL : https://hal.archives-ouvertes.fr/hal-00781393
Stringent error estimates for one-dimensional, space-dependent 2×2 relaxation systems, Ann. IHP (C) Nonlinear Analysis, vol.33, pp.621-654, 2016. ,
URL : https://hal.archives-ouvertes.fr/hal-01057737
Performance of numerical methods on the non-unique solution to the Riemann problem for the shallow water equations, Intern. J. Num. Meth. Fluids, vol.47, pp.825-831, 2005. ,
A fast and stable well-balanced scheme with hydrostatic reconstruction for shallow water flows, SIAM J. Sci. Comput, vol.25, pp.2050-2065, 2004. ,
Kinetic entropy inequality and hydrostatic reconstruction scheme for the Saint-Venant system, Math. Comput, vol.85, pp.2815-2837, 2016. ,
URL : https://hal.archives-ouvertes.fr/hal-01063577
A well-balanced positivity preserving second-order scheme for Shallow Water flows on unstructured meshes, J. Comput. Phys, vol.206, pp.311-333, 2005. ,
URL : https://hal.archives-ouvertes.fr/inria-00070738
A multilayer Saint-Venant system with mass exchanges for Shallow Water flows. Derivation and numerical validation, ESAIM, pp.169-200, 2011. ,
URL : https://hal.archives-ouvertes.fr/hal-00355730
Convergence of flux vector splitting schemes with single entropy inequality for hyperbolic systems of conservation laws, Numer. Math, vol.99, pp.585-604, 2005. ,
Kinetic invariant domains and relaxation limit from a BGK model to isentropic gas dynamics, Asymptotic Analysis, vol.31, pp.153-176, 2002. ,
Relaxation to isentropic gas dynamics for a BGK system with single kinetic entropy, Meth. Appl. Anal, vol.9, pp.313-327, 2002. ,
A fully well-balanced, positive and entropysatisfying Godunov-type method for the shallow-water equations, Math. Comput, vol.85, pp.1281-1307, 2016. ,
URL : https://hal.archives-ouvertes.fr/hal-00956799
A positive preserving high order VFRoe scheme for shallow water equations: a class of relaxation schemes, SIAM J. Scientific Comput, vol.30, pp.2587-2612, 2008. ,
URL : https://hal.archives-ouvertes.fr/hal-00370486
Entropy satisfying flux vector splittings and kinetic BGK models, Numer. Math, vol.94, pp.623-672, 2003. ,
Finite difference schemes with cross derivatives correctors for multidimensional parabolic systems, J. Hyp. Diff. Eq, vol.3, pp.27-52, 2006. ,
A multi well-balanced scheme for the shallow water MHD system with topography, Numer. Math, vol.136, pp.875-905, 2017. ,
URL : https://hal.archives-ouvertes.fr/hal-01131297
A subsonic-well-balanced reconstruction scheme for shallow water flows, Siam J. Numer. Anal, vol.48, pp.1733-1758, 2010. ,
URL : https://hal.archives-ouvertes.fr/hal-00693032
A robust well-balanced scheme for multi-layer shallow water equations, Discrete and Continuous Dynamical Systems B, vol.13, pp.739-758, 2010. ,
Well-balanced numerical schemes based on a generalized hydrostatic reconstruction technique, Math. Models Methods Appl. Sci, vol.17, pp.2065-2113, 2007. ,
A robust and entropy-satisfying numerical scheme for fluid flows in discontinuous nozzles, Math. Models Meth. Appl. Sci, vol.24, pp.2043-2083, 2014. ,
URL : https://hal.archives-ouvertes.fr/hal-00795446
Well-balanced schemes to capture non-explicit steady states: Ripa model, Math. Comp, vol.85, pp.1571-1602, 2016. ,
Convergence of approximate solutions to conservation laws, Archive Rational Mech. Anal, vol.82, pp.27-70, 1983. ,
Convergence of relaxation schemes to the equations of elastodynamics, Math. Comp, vol.70, pp.555-577, 2001. ,
Existence and stability of entropy solutions for the hyperbolic systems of isentropic gas dynamics in Eulerian and Lagrangian coordinates, Comm. Pure Applied Math, vol.49, pp.599-638, 1996. ,
Numerical methods for nonconservative hyperbolic systems: a theoretical framework, SIAM J. Numer. Anal, vol.44, pp.300-321, 2006. ,
A kinetic scheme for the Saint Venant system with a source term, Calcolo, vol.38, pp.201-231, 2001. ,
URL : https://hal.archives-ouvertes.fr/hal-00922664
Convergence of the upwind interface source method for hyperbolic conservation laws, Hyperbolic problems: theory, numerics, applications, pp.61-78, 2003. ,
URL : https://hal.archives-ouvertes.fr/hal-00922680
Compensated compactness and applications to partial differential equations, Nonlinear analysis and mechanics, Heriot-Watt symposium, vol.4, pp.136-211, 1979. ,
Well-posedness of scalar conservation laws with singular sources, Meth. Appl. Anal, vol.9, pp.291-312, 2002. ,
On the solution to the riemann problem for the compressible duct flow, SIAM J. Appl. Math, vol.64, pp.878-901, 2004. ,