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The convergence of the GRP scheme

2008
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Discrete and Continuous Dynamical Systems. Series A
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This paper deals with the convergence of the second-order GRP (Generalized Riemann Problem) numerical scheme to the entropy solution for scalar conservation laws with strictly convex fluxes. The approximate profiles at each time step are linear in each cell, with possible jump discontinuities (of functional values and slopes) across cell boundaries. The basic observation is that the discrete values produced by the scheme are exact averages of an approximate conservation law, which enables the

doi:10.3934/dcds.2009.23.1
fatcat:xd4lsv3erne7vfhvjmx5m34ce4