We study mixed-moment models (full zeroth moment, half higher moments) for a Fokker–Planck equation in one space dimension. Mixed-moment minimum-entropy models are known to overcome the zero net-flux problem of full-moment minimum-entropy Mn models. A realizability theory for these mixed moments of arbitrary order is derived, as well as a new closure, which we refer to as Kershaw closure. They ...

The fractal conservation law ∂tu + ∂x( f (u)) + (−∆)α/2u = 0 changes characteristics as α → 2 from non-local and weakly diffusive to local and strongly diffusive. In this paper we present a corrected finite difference quadrature method for (−∆)α/2 with α ∈ [0,2], combined with usual finite volume methods for the hyperbolic term, that automatically adjusts to this change and is uniformly converg...

We consider finite volume relaxation schemes for multidimensional scalar conservation laws. These schemes are constructed by appropriate discretization of a relaxation system and it is shown to converge to the entropy solution of the conservation law with a rate of h1/4 in L∞([0, T ], Lloc(R d)) .