Paper Info
Title
Optimal Rate of Convergence for Anisotropic Vanishing Viscosity Limit of a Scalar Balance Law
Abstract
An open question in numerical analysis of multidimensional scalar conservation laws discretized on nonstructured grids is the optimal rate of convergence. The main difficulty lies on a priori BV bounds which cannot be derived by opposition to the case of structured (Cartesian) grids. In this paper we consider a related question for a corresponding continuous model, namely, the vanishing viscosity method for a multidimensional scalar conservation law with a general diffusion matrix which is only bounded. Then BV estimates are not available here; nevertheless we prove the h(1/2) convergence rate. Our strategy of proof differs from the classical method of Kuznetsov. It consists in using in an accurate way the entropy dissipation due to the parabolic terms. The dissipation of the conservation law is not strong enough, and we thus consider an auxiliary parabolic problem to compensate that. Using the kinetic formulation and the related uniqueness method also helps to avoid unessential technicalities.
Year
DOI
Venue
2003
10.1137/S0036141002407995
SIAM JOURNAL ON MATHEMATICAL ANALYSIS
Keywords
Field
DocType
rate of convergence,vanishing viscosity method,kinetic formulation,scalar conservation laws
Discretization,Uniqueness,Mathematical analysis,Scalar (physics),Rate of convergence,Partial differential equation,Mathematics,Conservation law,Bounded function,Parabola
Journal
Volume
Issue
ISSN
34
6
0036-1410
Citations 
PageRank 
References 
0
0.34
1
Authors
2
Name
Order
Citations
PageRank
Charalambos Makridakis125348.36
Benoît Perthame200.34