Finite-difference methods for one-dimensional hyperbolic conservation laws

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Abstract

This article contains a survey of some important finite-difference methods for one-dimensional hyperbolic conservation laws. Weak solutions of hyperbolic conservation laws are introduced and the concept of entropy stability is discussed. Furthermore, the Riemann problem for hyperbolic conservation laws is solved. An introduction to finite-difference methods is given for which important concepts such as, e.g., conservativity, stability, and consistency are introduced. Godunov-type methods are elaborated for general systems of hyperbolic conservation laws. Finally, flux limiter methods are developed for the scalar nonlinear conservation law.
Original languageEnglish
Pages (from-to)225-269
Number of pages45
JournalNumerical Methods for Partial Differential Equations
Volume10
Issue number2
DOIs
Publication statusPublished - 1994

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