A priori error estimates for numerical methods for scalar conservation laws part III: Multidimensional flux-splitting monotone schemes on non-cartesian grids

Bernardo Cockburn, Pierre Alain Gremaud, Jimmy Xiangrong Yang

Research output: Contribution to journalArticlepeer-review

18 Scopus citations

Abstract

This paper is the third of a series in which a general theory of a priori error estimates for scalar conservation laws is constructed. In this paper, we consider multidimensional flux-splitting monotone schemes denned on non-Cartesian grids. We identify those schemes which are consistent and prove that the L (0, T; L1 (ℝd))-norm of the error goes to zero as (Δx)1/2 when the discretization parameter δx goes to zero. Moreover, we show that nonconsistent schemes can converge at optimal rates of (Δx)1/2 because (i) the conservation form of the schemes and (ii) the so-called consistency of the numerical fluxes allow the regularity properties of the approximate solution to compensate for their lack of consistency.

Original languageEnglish (US)
Pages (from-to)1775-1803
Number of pages29
JournalSIAM Journal on Numerical Analysis
Volume35
Issue number5
DOIs
StatePublished - 1998

Keywords

  • A priori error estimates
  • Conservation laws
  • Irregular grids
  • Monotone schemes
  • Supraconvergence

Fingerprint Dive into the research topics of 'A priori error estimates for numerical methods for scalar conservation laws part III: Multidimensional flux-splitting monotone schemes on non-cartesian grids'. Together they form a unique fingerprint.

Cite this