Convergence of the Upwind Interface Source Method for Hyperbolic Conservation Laws

Benoît Perthame () and Chiara Simeoni ()
Additional contact information
Benoît Perthame: École Normale Supérieure, Département de Mathématiques et Applications
Chiara Simeoni: École Normale Supérieure, Département de Mathématiques et Applications

A chapter in Hyperbolic Problems: Theory, Numerics, Applications, 2003, pp 61-78 from Springer

Abstract: Abstract This paper deals with typical questions arising in the analysis of numerical approximations for scalar conservation laws with a source term. We focus our attention on semi-discrete finite volume schemes, in the general case of a nonuniform spatial mesh. To define appropriate discretizations of the source term, we introduce the formalism peculiar to the Upwind Interface Source method and we establish conditions on the numerical functions so that the discrete solver preserves the steady state solutions. Then we formulate a rigorous definition of consistency, adapted to the class of well-balanced schemes, for which we are able to prove a Lax-Wendroff type convergence theorem. Some examples of numerical methods are discussed, in order to validate the arguments we propose.

Keywords: Source Term; Steady State Solution; Hyperbolic System; Entropy Solution; Entropy Inequality (search for similar items in EconPapers)
Date: 2003
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-55711-8_5

Ordering information: This item can be ordered from
http://www.springer.com/9783642557118

DOI: 10.1007/978-3-642-55711-8_5

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().