On numerical entropy inequalities for a class of relaxed schemes

H. Tang*, Tao Tang, J. Wang

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

2 Citations (Scopus)


In [4], Jin and Xin developed a class of first- and second-order relaxing schemes for nonlinear conservation laws. They also obtained the relaxed schemes for conservation laws by using a Hilbert expansion for the relaxing schemes. The relaxed schemes were proved to be total variational diminishing (TVD) in the zero relaxation limit for scalar equations. In this paper, by properly choosing the numerical entropy flux, we show that the relaxed schemes also satisfy the entropy inequalities. As a consequence, the L1 convergence rate of O (√Δt) for the relaxed schemes can be established.

Original languageEnglish
Pages (from-to)391-399
Number of pages9
JournalQuarterly of Applied Mathematics
Issue number2
Publication statusPublished - Jun 2001

Scopus Subject Areas

  • Applied Mathematics

User-Defined Keywords

  • Hyperbolic conservation laws
  • Numerical entropy inequality
  • Relaxed schemes
  • Relaxing schemes


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