Convergence rate approximate solutions to conservation laws with initial rarefactions

Haim Nessyahu, Tamir Tassa

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


The authors address the question of local convergence rate of conservative Lip+-stable approximations uepsilon(x,t) to the entropy solution u(x,t) of a genuinely nonlinear conservation law. This paper extends the previous results by including lip+ -unbounded initial data. Specifically, it is shown that for arbitrary LINF intersection BV initial data, u and its derivatives may be recovered with an almost optimal, modulo a spurious log factor, error of O(ε/Inε/). This analysis relies on obtaining new Lip+-stability estimates for the speed a(uε), rather than for uepsilon itself. This enables the establishment of an O(ε/Inε) convergence rate in W-1,1, which, in turn, implies the above mentioned local convergence rate.

Original languageEnglish
Pages (from-to)628-654
Number of pages27
JournalSIAM Journal on Numerical Analysis
Issue number3
StatePublished - 1 Jan 1994
Externally publishedYes

ASJC Scopus subject areas

  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics


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