Abstract. This paper addresses the recovery of piecewise smooth functions from their discrete data. Reconstruction methods using both pseudo-spectral coefficients and physical space interpolants have been discussed extensively in the literature, and it is clear that an a priori knowledge of the jump discontinuity location is essential for any reconstruction technique to yield spectrally accurat...

We use the kinetic approach of Perthame and Tadmor (1991) to calculate the error estimates for general scalar conservation laws governing problems in gas dynamics or fluid mechanics in general. The Kružkov and Kuznetsov techniques are generalized to this method, and an error bound of order √ ε (where ε is the mean free path) is obtained.

We discuss determination of jumps for functions with generalized bounded variation. The questions are motivated by A. Gelb and E. Tadmor [1], F. Móricz [5] and [6] and Q. L. Shi and X. L. Shi [7]. Corollary 1 improves the results proved in B. I. Golubov [2] and G. Kvernadze [3]. Ÿ

We study kinetic representations of flocking models. They arise from agent-based models for self-organized dynamics, such as Cucker-Smale [5] and Motsch-Tadmor [11] models. We prove the flocking behavior for the kinetic descriptions of flocking systems, which indicates a concentration in velocity variable in infinite time. We propose a discontinuous Galerkin method to treat the asymptotic δ -si...

Four explicit finite difference schemes, including Lax-Friedrichs, Nessyahu-Tadmor, Lax-Wendroff and Lax-Wendroff with a nonlinear filter are applied to solve water hammer equations. The schemes solve the equations in a reservoir-pipe-valve with an instantaneous and gradual closure of the valve boundary. The computational results are compared with those of the method of characteristics (MOC), a...

four explicit finite difference schemes, including lax-friedrichs, nessyahu-tadmor, lax-wendroff and lax-wendroff with a nonlinear filter are applied to solve water hammer equations. the schemes solve the equations in a reservoir-pipe-valve with an instantaneous and gradual closure of the valve boundary. the computational results are compared with those of the method of characteristics (moc), a...

A class of non-oscillatory numerical methods for solving nonlinear scalar conservation laws in one space dimension is considered. This class of methods contains the classical Lax-Friedrichs and the second order Nessyahu-Tadmor scheme. In the case of linear flux, new l2 stability results and error estimates for the methods are proved. Numerical experiments confirm that these methods are one-side...

We discuss an extension of the Jiang–Tadmor and Kurganov–Tadmor fully-discrete non-oscillatory central schemes for hyperbolic systems of conservation laws to unstructured triangular meshes. In doing so, we propose a new, ‘‘genuinely multidimensional,” non-oscillatory reconstruction—the minimum-angle plane reconstruction (MAPR). The MAPR is based on the selection of an interpolation stencil yiel...