Non-oscillatory schemes are widely used in numerical approximations of nonlinear conservation laws. The Nessyahu-Tadmor (NT) scheme is an example of a second order scheme that is both robust and simple. In this paper, we prove a new stability property of the NT scheme based on the standard minmod reconstruction in the case of a scalar strictly convex conservation law. This property is similar t...

The numerical integration of the hydrodynamical model of semiconductors based on Extended Thermodynamics has been tackled. On account of the mathematical complexity of the system no theoretical conditions of convergence are available for the existing schemes. Therefore in order to lend conndence to the obtained numerical solution it was almost mandatory to resort to a cross-validation comparing...

A hydrodynamical model based on the theory of extended thermodynamics is presented for carrier transport in semiconductors. Closure relations for fluxes are obtained by employing the maximum entropy principle. The production terms are modeled by fitting the Monte Carlo data for homogeneously doped semiconductors. The mathematical properties of the model are studied. A suitable numerical method,...

In this paper, we consider several high order schemes in one space dimension. In particular, we compare the second order relaxation (<<1) or "relaxed" (=0) schemes of Jin-Xin 4], with the second order Lax-Friedrichs scheme of Nessyahu-Tadmor 6], and with higher order ENO and WENO schemes. This comparison is rst made on Sod shock tube, and then on a very pathological example of a p-system constr...

We show the discrete lip+-stability for a relaxation scheme proposed by Jin and Xin [Comm. Pure Appl. Math., 48 (1995), pp. 235–277] to approximate convex conservation laws. Equipped with the lip+-stability we obtain global error estimates in the spaces W s,p for −1 ≤ s ≤ 1/p, 1 ≤ p ≤ ∞ and pointwise error estimates for the approximate solution obtained by the relaxation scheme. The proof uses ...

Central schemes may serve as universal finite-difference methods for solving nonlinear convection–diffusion equations in the sense that they are not tied to the specific eigenstructure of the problem, and hence can be implemented in a straightforward manner as black-box solvers for general conservation laws and related equations governing the spontaneous evolution of large gradient phenomena. T...

The central scheme of Nessyahu and Tadmor (J. Comput. Phys, 87(1990)) has the benefit of not having to deal with the solution within the Riemann fan for solving hyperbolic conservation laws and related equations. But the staggered averaging causes large dissipation when the time step size is small comparing to the mesh size. The recent work of Kurganov and Tadmor (J. Comput. Phys, 160(2000)) ov...

There has been an enormous amount of work on error estimates for approximate solutions to scalar conservation laws. The methods of analysis include matching the traveling wave solutions, [8, 24]; matching the Green function of the linearized problem [21]; weak W convergence theory [32]; the Kruzkov-functional method [19]; and the energy-like method [34]. The results on error estimates include: ...

Many second order accurate non-oscillatory schemes are based on the Minmod limiter, for example the Nessyahu-Tadmor scheme. It is well known that the Lperror of monotone finite difference methods for the linear advection equation is of order 1/2 for initial data in W (Lp), 1 ≤ p ≤ ∞, see [2]. For a second or higher order non-oscillatory schemes very little is known because they are nonlinear ev...

We present a new formulation of three-dimensional central finite volume methods on unstructured staggered grids for solving systems of hyperbolic equations. Based on the Lax-Friedrichs and Nessyahu-Tadmor one-dimensional central finite difference schemes, the numerical methods we propose involve a staggered grids in order to avoid solving Riemann problems at cell interfaces. The cells are baryc...