On the convergence of difference approximations to scalar conservation laws

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Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, For sale by the National Technical Information Service , Hampton, Va, [Springfield, Va
Conservation laws (Mathema
StatementStanley Osher and Eitan Tadmor.
SeriesICASE report -- no. 85-28., NASA contractor report -- 172614., NASA contractor report -- NASA CR-172614.
ContributionsTadmor, Eitan., Institute for Computer Applications in Science and Engineering.
The Physical Object
FormatMicroform
Pagination1 v.
ID Numbers
Open LibraryOL15276914M

On the Convergence of Difference Approximations to Scalar Conservation Laws* By Stanley Osher and Eitan Tadmor Abstract. We present a unified treatment of explicit in time, two-level, second-order resolution (SOR), total-variation diminishing (TVD), approximations to scalar conser-vation laws.

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SIAM Journal on Numerical AnalysisAbstract | PDF ( KB) () Pointwise convergence rate of vanishing viscosity approximations for scalar conservation laws with by: Get this from a library. On the convergence of difference approximations to scalar conservation laws.

[Stanley Osher; Eitan Tadmor; Institute for Computer Applications in Science and Engineering.]. Monotone Difference Approximations for Scalar Conservation Laws By Michael G. Crandall and Andrew Majda* Abstract. A complete self-contained treatment of the stability and convergence proper-ties of conservation-form, monotone difference approximations to scalar conservation laws in several space variables is developed.

Abstract. We develop a general framework for the analysis of approximations to stochastic scalar conservation laws. Our aim is to prove, under minimal consistency properties and bounds, that such approximations are converging to the solution to a stochastic scalar conservation by: 6. Flow of two phases in a heterogeneous porous medium is modeled by a scalar conservation law with a discontinuous coefficient.

As solutions of conservation laws with discontinuous coefficients depend explicitly on the underlying small scale effects, we consider a model where the relevant small scale effect is dynamic capillary pressure.

We prove that the limit of vanishing dynamic capillary Cited by: Convergence of vanishing capillarity approximations for scalar conservation laws with discontinuous fluxes Article in Networks and Heterogeneous Media 4(4) December with 24 Reads.

Convergence is established for a scalar finite difference scheme, based on the Godunov or Engquist--Osher (EO) flux, for scalar conservation laws having a flux that is spatially dependent through a possibly discontinuous coefficient.

Other works in this direction have established convergence for methods employing the solution of 2 × 2 Riemann by: H. Nessyahu and E. Tadmor, The convergence rate of approximate solutions for nonlinear scalar conservation laws, SIAM J. Numer.

Anal., 29 (), – Cited by: 4.

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A complete self-contained treatment of the stability and convergence properties of conservation-form, monotone difference approximations to scalar conservation laws in several space variables is. A convergence theory for semi-discrete approximations to nonlinear systems of conservation laws is developed.

It is shown, by a series of scalar counter-examples, that consistency with the conservation law alone does not guarantee convergence. Zheng Ran, Galilean invariance and the conservative difference schemes for scalar laws, Advances in Difference Equations, /,1, ().

Crossref Zhen-huan Teng, Exact boundary conditions for the initial value problem of convex conservation laws, Journal of Computational Physics,10, (), ().Cited by: nasa-cr l _____ __ on the convergence of difference approximations to scalar conservation laws stanley osher eltan tadmor contract no.

nasl may langley research center library, nasa hampton, virginia institute for co~~uter applications in science and engineering. n 0;i2Z are good approximations of the values of the solution uto ().

This is however not the case because, except in some trivial cases (c= 0 or u 0 constant, for example), [(),()] does not respect a fundamental feature of scalar conservation laws (linear or non-linear):File Size: KB.

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A convergence theory for semi-discrete approximations to nonlinear systems of conservation laws is developed. It is shown, by a series of scalar counter-examples, that consistency with the conservation law alone does not guarantee convergence.

Instead, a notion of consistency which takes into. In physics, a conservation law states that a particular measurable property of an isolated physical system does not change as the system evolves over time. Exact conservation laws include conservation of energy, conservation of linear momentum, conservation of angular momentum, and conservation of electric are also many approximate conservation laws, which apply to such quantities.

Finite difference and finite volume methods for transport and conservation laws Boualem Khouider PIMS summer school on stochastic and probabilistic methods for atmosphere, ocean, and dynamics.

University of Victoria, JulyContents 1 Introduction to finite differences: The heat equation 4File Size: KB. We prove the convergence of the explicit-in-time Finite Volume method with monotone fluxes for the approximation of scalar first-order conservation laws with multiplicative, compactly supported by: 3.

Convergence of Approximate Solutions to Conservation Laws R. DiPerna We shall discuss some results on the theoretical side of conservation laws concerning the convergence of approximate solutions. u The general setting is a system of n conservation laws in one space dimension t + f(u) x = °' and Rn.

f to We shall assume that f (1) where u = u(x,t) e R n Rn is a smooth nonlinear is n Cited by: 1. CONVERGENCE RATE OF APPROXIMATE SOLUTIONS TO CONSERVATION LAWS WITH INITIAL RAREFACTIONS ⁄ HAIM NESSYAHU yAND TAMIR TASSA Abstract.

We address the question of local convergence rate of conservative Lip+-stable approximations, u"(x;t), to the entropy solution, u(x;t), of a genuinely nonlinear conservation question has been answered in the case of rarefaction.

The difference equation () is written in conservation form. Lax and Wendroff [11] showed that to satisfy the integral form of the conservation laws it suffices to approximate them by difference equations in conservation form.

For example, the well-known one-sided difference approximation to File Size: 2MB. REGULARITY THROUGH APPROXIMATION FOR SCALAR CONSERVATION LAWS∗ BRADLEY J.

LUCIER† Abstract. In this paper it is shown that recent approximation results for scalar conservation laws in one space dimension imply that solutions of these equations with smooth, convex fluxes have more regularity than previously by: 7.

Lyapunov stability analysis of networks of scalar conservation laws. Networks & Heterogeneous Media,2 (4): doi: /nhm [3] Wen Shen. Traveling waves for conservation laws with nonlocal flux for traffic flow on rough by: 4. for solving partial differential equations.

The focuses are the stability and convergence theory. The partial differential equations to be discussed include •parabolic equations, •elliptic equations, •hyperbolic conservation laws. Finite Difference Approximation Our goal is to appriximate differential operators by finite difference File Size: KB.

L1-dissipativity for scalar conservation laws 3 Analysis in terms of Riemann solvers 4 Admissibility germs and uniqueness 5 Measure-valued G-entropy solutions and convergence results 7 Outline of the paper 7 2. Preliminaries 8 3. The model one-dimensional problem 9 De nitions of germs and their basic properties 10   Shareable Link.

Use the link below to share a full-text version of this article with your friends and colleagues. Learn more. Convergence of upwind finite difference algorithms for scalar conservation laws with indefinite discontinuitites in the flux function. Toth and B. Valko: Perturbation of singular equilibria of hyperbolic two-component systems: a universal hydrodynamic limit.

This is necessary to pass into the limit inside the nonlinear term axu"). Section 3 deals with the convergence of a". First of all we let 8 - 0, and we get the existence for the problem (Ps), then we let a -0 and, by the methods of compensated compactness, we prove the convergence to an entropy solution of the scalar conservation law (P).Cited by: Abstract.

In this paper we consider numerical approximations of hyperbolic conservation laws in the one-dimensional scalar case, by studying Godunov and van Leer’s methods. Before to present the numerical treatment of hyperbolic conservation laws, a theoretical introduction is given together with the definition of the Riemann problem.

The convergence analysis in Lp loc (p Cited by:. Finite Volume Methods for Scalar Conservation Laws on Time Dependent Meshes O. Havle Charles University, Faculty of Mathematics and Physics, Prague, Czech Republic. Abstract. Finite volume method is a method of choice for hyperbolic systems of conservation laws such as the Euler equations of gas dynamics.

FVM is often.CONVERGENCE OF FINITE VOLUME SCHEMES FOR TRIANGULAR SYSTEMS OF CONSERVATION LAWS K. H. KARLSEN, S. MISHRA, AND N. H. RISEBRO Abstract. We consider non-strictly hyperbolic systems of conservation laws in triangular form, which arise in applications like three-phase flows in porous media.Convergence properties of the SWR method applied to convection dominated viscous conservation laws with nonlinear ux are given in [15].

This work is a contribution to the non-overlapping case in dealing with a new space-time DDM for scalar conservation laws without viscous terms and using the STILSAuthor: S. Doucoure.