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Error Estimates for Well-Balanced Schemes on Simple Balance Laws = One-Dimensional Position-Dependent Models /

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Error Estimates for Well-Balanced Schemes on Simple Balance Laws/ by Debora Amadori, Laurent Gosse.
Reminder of title:	One-Dimensional Position-Dependent Models /
Author:	Amadori, Debora.
other author:	Gosse, Laurent.
Description:	XV, 110 p. 24 illus., 15 illus. in color.online resource. :
Contained By:	Springer Nature eBook
Subject:	Partial differential equations. -
Online resource:	https://doi.org/10.1007/978-3-319-24785-4
ISBN:	9783319247854

Error Estimates for Well-Balanced Schemes on Simple Balance Laws = One-Dimensional Position-Dependent Models /
Amadori, Debora.

Error Estimates for Well-Balanced Schemes on Simple Balance LawsOne-Dimensional Position-Dependent Models /[electronic resource] :by Debora Amadori, Laurent Gosse. - 1st ed. 2015. - XV, 110 p. 24 illus., 15 illus. in color.online resource. - SpringerBriefs in Mathematics,2191-8198. - SpringerBriefs in Mathematics,.

1 Introduction -- 2 Local and global error estimates -- 3 Position-dependent scalar balance laws -- 4 Lyapunov functional for inertial approximations -- 5 Entropy dissipation and comparison with Lyapunov estimates -- 6 Conclusion and outlook.

This monograph presents, in an attractive and self-contained form, techniques based on the L1 stability theory derived at the end of the 1990s by A. Bressan, T.-P. Liu and T. Yang that yield original error estimates for so-called well-balanced numerical schemes solving 1D hyperbolic systems of balance laws. Rigorous error estimates are presented for both scalar balance laws and a position-dependent relaxation system, in inertial approximation. Such estimates shed light on why those algorithms based on source terms handled like "local scatterers" can outperform other, more standard, numerical schemes. Two-dimensional Riemann problems for the linear wave equation are also solved, with discussion of the issues raised relating to the treatment of 2D balance laws. All of the material provided in this book is highly relevant for the understanding of well-balanced schemes and will contribute to future improvements.

ISBN: 9783319247854

Standard No.: 10.1007/978-3-319-24785-4doiSubjects--Topical Terms:

1102982
Partial differential equations.

LC Class. No.: QA370-380

Dewey Class. No.: 515.353

Error Estimates for Well-Balanced Schemes on Simple Balance Laws = One-Dimensional Position-Dependent Models /
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