A system of conservation laws including a stiff relaxation term; The 2D case

Wen Shen, Aslak Tveito, Ragnar Winther

Research output: Contribution to journalArticle

5 Scopus citations

Abstract

We analyze a system of conservation laws in two space dimensions with a stiff relaxation term. A semi-implicit finite difference method approximating the system is studied and an error bound of order script O sign(√Δt) measured in L1 is derived. This error bound is independent of the relaxation time δ > 0. Furthermore, it is proved that the solutions of the system converge towards the solution of an equilibrium model as the relaxation time δ tends to zero, and that the rate of convergence measured in L1 is of order script O sign(δ1/3). Finally, we present some numerical illustrations.

Original languageEnglish (US)
Pages (from-to)786-813
Number of pages28
JournalBIT Numerical Mathematics
Volume36
Issue number4
DOIs
StatePublished - Jan 1 1996

All Science Journal Classification (ASJC) codes

  • Software
  • Computer Networks and Communications
  • Computational Mathematics
  • Applied Mathematics

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