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＜E-Book＞
Error Estimates for Well-Balanced Schemes on Simple Balance Laws : One-Dimensional Position-Dependent Models / by Debora Amadori, Laurent Gosse
(SpringerBriefs in Mathematics. ISSN:21918201)

Edition	1st ed. 2015.
Publisher	(Cham : Springer International Publishing : Imprint: Springer)
Year	2015
Size	XV, 110 p. 24 illus., 15 illus. in color : online resource
Authors	*Amadori, Debora author Gosse, Laurent author SpringerLink (Online service)
Subjects	LCSH:Differential equations LCSH:Numerical analysis LCSH:Mathematical physics FREE:Differential Equations FREE:Numerical Analysis FREE:Mathematical Physics FREE:Theoretical, Mathematical and Computational Physics
Notes	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 HTTP:URL=https://doi.org/10.1007/978-3-319-24785-4

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