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


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 \(\big\| u^\ve(t,\cdot)-u(t,\cdot)\big\|_{{\bf L}^1} %{\strut\L^1}=o(1)\cdot \sqrt{\Delta x} \big|\ln (\Delta x)\big|.\)


Viscosity Approximate Solution Mesh Size Viscosity Solution Error Bound 
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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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