EAN: 9783319247847

SPRINGERBRIEFS IN MATHEMATICS ERROR ESTIMATES...

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.

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