Stability and convergence of a class of finite element schemes for hyperbolic systems of conservation laws

Christos Arvanitis*, Charalambos Makridakis, Athanasios Tzavaras

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

15 Scopus citations

Abstract

We propose a class of finite element schemes for systems of hyperbolic conservation laws that are based on finite element discretizations of appropriate relaxation models. We consider both semidiscrete and fully discrete finite element schemes and show that the schemes are stable and, when the compensated compactness theory is applicable, do converge to a weak solution of the hyperbolic system. The schemes use piecewise polynomials of arbitrary degree and their consistency error is of high order. We also prove that the rate of convergence of the relaxation system to a smooth solution of the conservation laws is of order O(ε).

Original languageEnglish (US)
Pages (from-to)1357-1393
Number of pages37
JournalSIAM Journal on Numerical Analysis
Volume42
Issue number4
DOIs
StatePublished - Dec 1 2004

Keywords

  • Adaptive schemes
  • Finite element schemes
  • Hyperbolic conservation laws
  • Stability and convergence

ASJC Scopus subject areas

  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics

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