Hoff, David; Smoller, Joel Error bounds for Glimm difference approximations for scalar conservation laws. (English) Zbl 0579.65096 Trans. Am. Math. Soc. 289, 611-642 (1985). This paper treats the Glimm difference approximation to the solution of a genuinely nonlinear scalar conservation law \(v_ t+f(v)_ x==0\), \((x,t)\in R\times R_+\), with initial data \(v(x,0)=v_ o(x)\) with bounded variation. Error bounds for this problem are derived in the general case and for the generic case of piecewise constant initial data. Reviewer: V.Drápalík Cited in 2 ReviewsCited in 4 Documents MSC: 65M15 Error bounds for initial value and initial-boundary value problems involving PDEs 35L65 Hyperbolic conservation laws Keywords:Glimm; nonlinear; piecewise constant initial data PDF BibTeX XML Cite \textit{D. Hoff} and \textit{J. Smoller}, Trans. Am. Math. Soc. 289, 611--642 (1985; Zbl 0579.65096) Full Text: DOI OpenURL References: [1] James Glimm, Solutions in the large for nonlinear hyperbolic systems of equations, Comm. Pure Appl. Math. 18 (1965), 697 – 715. · Zbl 0141.28902 [2] James Glimm and Peter D. Lax, Decay of solutions of systems of nonlinear hyperbolic conservation laws, Memoirs of the American Mathematical Society, No. 101, American Mathematical Society, Providence, R.I., 1970. · Zbl 0204.11304 [3] S. N. Krushkov, First order quasilinear equations in several space variables, Math. USSR Sb. 10 (1970), 217-273. [4] L. Kuipers and H. Niederreiter, Uniform distribution of sequences, Wiley-Interscience [John Wiley & Sons], New York-London-Sydney, 1974. Pure and Applied Mathematics. · Zbl 0281.10001 [5] N. N. Kuznetsov, On stable methods for solving non-linear first order partial differential equations in the class of discontinuous functions, Topics in numerical analysis, III (Proc. Roy. Irish Acad. Conf., Trinity Coll., Dublin, 1976) Academic Press, London, 1977, pp. 183 – 197. [6] Tai Ping Liu, The deterministic version of the Glimm scheme, Comm. Math. Phys. 57 (1977), no. 2, 135 – 148. · Zbl 0376.35042 [7] Joel Smoller, Shock waves and reaction-diffusion equations, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Science], vol. 258, Springer-Verlag, New York-Berlin, 1983. · Zbl 0508.35002 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.