Error Estimates for Well-Balanced Schemes on Simple Balance Laws

Error Estimates for Well-Balanced Schemes on Simple Balance Laws

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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 qlocal scatterersq 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.DCDS-B 9, 559a€“576 (2003) T. Li, W. Sheng, The general Riemann problem for the linearized system of ... 129, 129a€“145 (1995) R.E. Mickens, Applications of Nonstandard Finite Difference Schemes (World Scientific, Singapore, 2000) S. ... Physics 9(3), 688a€“710 (2010) M.H. Pham, M. Rudgyard, E. Sa#39;uli, Bicharacteristic methods for multi-dimensional hyperbolic ... AP] 7 Apr 2013 Y. Zheng, Systems of Conservation Laws: Two-Dimensional Riemann Problems, Progress in Nonlinear anbsp;...

Title:Error Estimates for Well-Balanced Schemes on Simple Balance Laws
Author: Debora Amadori, Laurent Gosse
Publisher:Springer - 2015-10-23

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