Convergence of MUSCL relaxing schemes to the relaxed schemes for conservation laws with stiff source terms

Tao Tang*, Jinghua Wang

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

6 Citations (Scopus)
4 Downloads (Pure)

Abstract

We consider the convergence and stability property of MUSCL relaxing schemes applied to conservation laws with stiff source terms. The maximum principle for the numerical schemes will be established. It will be also shown that the MUSCL relaxing schemes are uniformly l1- and TV-stable in the sense that they are bounded by a constant independent of the relaxation parameter ε, the Lipschitz constant of the stiff source term and the time step Δt. The Lipschitz constant of the l1 continuity in time for the MUSCL relaxing schemes is shown to be independent of ε and Δt. The convergence of the relaxing schemes to the corresponding MUSCL relaxed schemes is then established.

Original languageEnglish
Pages (from-to)173-195
Number of pages23
JournalJournal of Scientific Computing
Volume15
Issue number2
DOIs
Publication statusPublished - Jun 2000

Scopus Subject Areas

  • Software
  • Theoretical Computer Science
  • Numerical Analysis
  • Engineering(all)
  • Computational Theory and Mathematics
  • Computational Mathematics
  • Applied Mathematics

User-Defined Keywords

  • relaxation scheme
  • nonlinear conservation laws
  • maximum principle
  • convergence

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