TVB runge-kutta local projection discontinuous galerkin finite element method for conservation laws III: One-dimensional systems

Bernardo Cockburn, San Yih Lin, Chi Wang Shu

Research output: Contribution to journalArticle

912 Citations (Scopus)

Abstract

This is the third paper in a series in which we construct and analyze a class of TVB (total variation bounded) discontinuous Galerkin finite element methods for solving conservation laws uti=1d(fi(u)xi=0. In this paper we present the method in a system of equations, stressing the point of how to use the weak form in the component spaces, but to use the local projection limiting in the characteristic fields, and how to implement boundary conditions. A 1-dimensional system is thus chosen as a model. Different implementation techniques are discussed, theories analogous to scalar cases are proven for linear systems, and numerical results are given illustrating the method on nonlinear systems. Discussions of handling complicated geometries via adaptive triangle elements will appear in future papers.

Original languageEnglish
Pages (from-to)90-113
Number of pages24
JournalJournal of Computational Physics
Volume84
Issue number1
DOIs
Publication statusPublished - 1989 Sep

All Science Journal Classification (ASJC) codes

  • Numerical Analysis
  • Modelling and Simulation
  • Physics and Astronomy (miscellaneous)
  • Physics and Astronomy(all)
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics

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