Error bounds for a deterministic version of the Glimm scheme

Alberto Bressan, Andrea Marson

Research output: Contribution to journalArticle

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Abstract

Consider the hyperbolic system of conservation laws ut + F(u)x = 0. Let u be the unique viscosity solution with initial condition u(0, x) = ū(x), and let uε be an approximate solution constructed by the Glimm scheme, corresponding to the mesh sizes Δx, Δt = O(Δx). With a suitable choice of the sampling sequence, we prove the estimate ∥uε(t, ·) - u(t, ·)∥L = o(1) · √Δx|ln(Δx)|.

Original languageEnglish (US)
Pages (from-to)155-176
Number of pages22
JournalArchive for Rational Mechanics and Analysis
Volume142
Issue number2
DOIs
Publication statusPublished - May 28 1998

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All Science Journal Classification (ASJC) codes

  • Analysis
  • Mathematics (miscellaneous)
  • Mechanical Engineering

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