Quasimonotone schemes for scalar conservation laws. Part II

Bernardo Cockburn

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Abstract

In this paper, the technique of construction and analysis of quasimonotone finite-difference numerical schemes for scalar conservation laws in one space dimension, developed in Part I, is extended to a wide class of Petrov-Galerkin finite-element methods. The resulting schemes are called the quasimonotone finite-element schemes. The approximate solution is written as ūh + ūh, where ūh is a piecewise-constant function. The Petrov-Galerkin methods are then considered to be a set of equations that defines 'the parameter' ūh, plus a single equation, which is essentially a finite-difference scheme, that defines 'the means' ūh. All the results of the theory of quasimonotone finite-difference schemes can be carried over this finite-element framework by this simple point of view.

Original languageEnglish (US)
Pages (from-to)247-258
Number of pages12
JournalSIAM Journal on Numerical Analysis
Volume27
Issue number1
DOIs
StatePublished - 1990

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