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Overview"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." Full Product DetailsAuthor: Debora Amadori , Laurent GossePublisher: Springer International Publishing AG Imprint: Springer International Publishing AG Edition: 1st ed. 2015 Dimensions: Width: 15.50cm , Height: 0.70cm , Length: 23.50cm Weight: 2.058kg ISBN: 9783319247847ISBN 10: 3319247840 Pages: 110 Publication Date: 23 November 2015 Audience: College/higher education , Postgraduate, Research & Scholarly Format: Paperback Publisher's Status: Active Availability: Manufactured on demand We will order this item for you from a manufactured on demand supplier. Table of Contents1 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.ReviewsAll of the material provided in this book is highly relevant for the understanding of well-balanced schemes and will contribute to future improvements. Each chapter is more or less self-containing, it has its own abstract, introduction and the list of references. (Vit Dolejsi, zbMATH 1332.65132, 2016) Author InformationTab Content 6Author Website:Countries AvailableAll regions |