Pointwise error estimates for relaxation approximations to conservation laws

Eitan Tadmor*, Tao TANG

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

24 Citations (Scopus)

Abstract

We obtain sharp pointwise error estimates for relaxation approximation to scalar conservation laws with piecewise smooth solutions. We first prove that the first-order partial derivatives for the perturbation solutions are uniformly upper bounded (the so-called Lip+ stability). A one-sided interpolation inequality between classical L1 error estimates and Lip+ stability bounds enables us to convert a global L1 result into a (nonoptimal) local estimate. Optimal error bounds on the weighted error then follow from the maximum principle for weakly coupled hyperbolic systems. The main difficulties in obtaining the Lip+ stability and the optimal pointwise errors are how to construct appropriate "difference functions" so that the maximum principle can be applied.

Original languageEnglish
Pages (from-to)870-886
Number of pages17
JournalSIAM Journal on Mathematical Analysis
Volume32
Issue number4
DOIs
Publication statusPublished - 2000

Scopus Subject Areas

  • Analysis
  • Computational Mathematics
  • Applied Mathematics

User-Defined Keywords

  • Conservation laws
  • Error estimates
  • Maximum principle
  • One-sided interpolation inequality
  • Optimal convergence rate
  • Relaxation method

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