We discuss the concentration factor methods for determination of jumps in terms of spectral data. The results are relative to the classical Lukács Theorem and some recent results obtained by A. Gelb, E. Tadmor and F. Móricz. §

We improve the recent result of Chae and Tadmor (2008) [10] proving a one-sided threshold condition which leads to a finite-time breakdown of the Euler–Poisson equations in arbitrary dimension n. © 2009 Elsevier B.V. All rights reserved.

Nonoscillatory central schemes are a class of Godunov-type (i.e., shock-capturing, finite volume) numerical methods for solving hyperbolic systems of conservation laws (e.g., the Euler equations of gas dynamics). Throughout the last decade, central (Godunov-type) schemes have gained popularity due to their simplicity and efficiency. In particular, the latter do not require the solution of a Rie...

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...

In this dissertation we present two kinds of multidimensional schemes for hyperbolic systems based on triangular meshes. The first kind of schemes are evolution Galerkin schemes (EG) which are truly multidimensional schemes and the second kind is a new space-time conservative central-type method which we name a slope propagation (SP) method. Our first scheme is an extension of the EG schemes fo...

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...

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...