Tvb runge-kutta local projection discontinuous galerkin finite element method for conservation laws ii: General framework

Bernardo Cockburn, Chi Wang Shu

Research output: Contribution to journalArticlepeer-review

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Abstract

This is the second 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 ut+ ∑i=1d(fi(u))xi=0. In this paper we present a general framework of the methods, up to any order of formal accuracy, using scalar one-dimensional initial value and initial-boundary problems as models. In these cases we prove TVBM (total variation bounded in the means), TVB, and convergence of the schemes. Numerical results using these methods are also given. Extensions to systems and/or higher dimensions will appear in future papers.

Original languageEnglish (US)
Pages (from-to)411-435
Number of pages25
JournalMathematics of Computation
Volume52
Issue number186
DOIs
StatePublished - Apr 1989

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