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Archive for Rational Mechanics and Analysis

, Volume 142, Issue 2, pp 155–176 | Cite as

Error Bounds for a Deterministic Version of the Glimm Scheme

  • Alberto Bressan
  • Andrea Marson
Article

Abstract.

Consider the hyperbolic system of conservation laws \(u_t+F(u)_x=0\). Let u be the unique viscosity solution with initial condition \(u(0,x)=\bar u(x)\), and let u ε be an approximate solution constructed by the Glimm scheme, corresponding to the mesh sizes \(\Delta x$, $\Delta t =O(\Delta x)\). With a suitable choice of the sampling sequence, we prove the estimate \(\big\| u^\ve(t,\cdot)-u(t,\cdot)\big\|_{{\bf L}^1} %{\strut\L^1}=o(1)\cdot \sqrt{\Delta x} \big|\ln (\Delta x)\big|.\)

Keywords

Viscosity Approximate Solution Mesh Size Viscosity Solution Error Bound 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Alberto Bressan
    • 1
  • Andrea Marson
    • 2
  1. 1.S.I.S.S.A., Via Beirut 4, 34014 Trieste, ItalyIT
  2. 2.Università di Brescia, Dipartimento di Elettronica, per l'Automazione, Via Branze 38, 25123 Brescia, ItalyIT

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