In this paper we address the questions of the convergence rate for approximate solutions to conservation laws with piecewise smooth solutions in a weighted W 1,1 space. Convergence rate for the derivative of the approximate solutions is established under the assumption that a weak pointwise-error estimate is given. In other words, we are able to convert weak pointwise-error estimates to optimal...

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...

The aim of this paper is to present a streamlined and fully three-dimensional version of the quasicontinuum (QC) theory of Tadmor et al. [18, 19] and to analyze its accuracy and convergence characteristics. Specifically, we assess the effect of the summation rules on accuracy; we determine the rate of convergence of the method in the presence of strong singularities, such as point loads; and we...

Tadmor, Nezzar and Vese [Eitan Tadmor, Suzanne Nezzar, and Luminita Vese. A multiscale image representation using hierarchical (BV, L2) decompositions. Multiscale Model. Simul., 2(4):554–579, 2004.] developed a total variation based multiscale method for decomposing a function f ∈ BV into a countable set of features {uk : k = 0, 1, 2 . . .} associated to a sequence of dyadic scales {λk = λ02−k ...

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.

We consider the hydrodynamic limit of a collisionless and non-diffusive kinetic equation under strong local alignment regime. The local alignment is first considered by Karper, Mellet and Trivisa in [24], as a singular limit of an alignment force proposed by Motsch and Tadmor in [32]. As the local alignment strongly dominate, a weak solution to the kinetic equation under consideration converges...

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,...

We develop a simple energy method for proving the stability of finite difference schemes for multidimensional hyperbolic initial-boundary value problems. In particular, we extend to several space dimensions and to variable coefficients a crucial stability result by Goldberg and Tadmor for Dirichlet boundary conditions. This allows us to give some conditions on the discretized operator that ensu...