Displaying similar documents to “Consistency, accuracy and entropy behaviour of remeshed particle methods”

Monotone (A,B) entropy stable numerical scheme for Scalar Conservation Laws with discontinuous flux

Adimurthi, Rajib Dutta, G. D. Veerappa Gowda, Jérôme Jaffré (2014)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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For scalar conservation laws in one space dimension with a flux function discontinuous in space, there exist infinitely many classes of solutions which are contractive. Each class is characterized by a connection () which determines the interface entropy. For solutions corresponding to a connection (), there exists convergent numerical schemes based on Godunov or Engquist−Osher schemes. The natural question is how to obtain schemes, corresponding to computationally less...

Convergence of finite difference schemes for viscous and inviscid conservation laws with rough coefficients

Kenneth Hvistendahl Karlsen, Nils Henrik Risebro (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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We consider the initial value problem for degenerate viscous and inviscid scalar conservation laws where the flux function depends on the spatial location through a "rough"coefficient function . We show that the Engquist-Osher (and hence all monotone) finite difference approximations converge to the unique entropy solution of the governing equation if, among other demands, is in , thereby providing alternative (new) existence proofs for entropy solutions of degenerate...

Consistency, accuracy and entropy behaviour of remeshed particle methods

Lisl Weynans, Adrien Magni (2012)

ESAIM: Mathematical Modelling and Numerical Analysis

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In this paper we analyze the consistency, the accuracy and some entropy properties of particle methods with remeshing in the case of a scalar one-dimensional conservation law. As in [G.-H. Cottet and L. Weynans, (2006) 51–56] we re-write particle methods with remeshing in the finite-difference formalism. This allows us to prove the consistency of these methods, and accuracy properties related to the accuracy of interpolation kernels....

Measuring the Irreversibility of Numerical Schemes for Reversible Stochastic Differential Equations

Markos Katsoulakis, Yannis Pantazis, Luc Rey-Bellet (2014)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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For a stationary Markov process the detailed balance condition is equivalent to the time-reversibility of the process. For stochastic differential equations (SDE’s), the time discretization of numerical schemes usually destroys the time-reversibility property. Despite an extensive literature on the numerical analysis for SDE’s, their stability properties, strong and/or weak error estimates, large deviations and infinite-time estimates, no quantitative results are known on the lack of...

Entropy maximization and the busy period of some single-server vacation models

Jesus R. Artalejo, Maria J. Lopez-Herrero (2010)

RAIRO - Operations Research

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In this paper, information theoretic methodology for system modeling is applied to investigate the probability density function of the busy period in vacation models operating under the -, - and -policies. The information about the density function is limited to a few mean value constraints (usually the first moments). By using the maximum entropy methodology one obtains the least biased probability density function satisfying the system's constraints. The analysis of the three controllable...

On the connection between some Riemann-solver free approaches to the approximation of multi-dimensional systems of hyperbolic conservation laws

Tim Kröger, Sebastian Noelle, Susanne Zimmermann (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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In this paper, we present some interesting connections between a number of Riemann-solver free approaches to the numerical solution of multi-dimensional systems of conservation laws. As a main part, we present a new and elementary derivation of Fey's Method of Transport (MoT) (respectively the second author's ICE version of the scheme) and the state decompositions which form the basis of it. The only tools that we use are quadrature rules applied to the moment integral...