By Debora Amadori,Laurent Gosse
This monograph offers, in an enticing and self-contained shape, options in response to the L1 balance conception derived on the finish of the Nineteen Nineties via A. Bressan, T.-P. Liu and T. Yang that yield unique blunders estimates for so-called well-balanced numerical schemes fixing 1D hyperbolic structures of stability legislation. Rigorous mistakes estimates are awarded for either scalar stability legislation and a position-dependent rest approach, in inertial approximation. Such estimates make clear why these algorithms according to resource phrases dealt with like "local scatterers" can outperform different, extra common, numerical schemes. Two-dimensional Riemann difficulties for the linear wave equation also are solved, with dialogue of the problems raised in relation to the remedy of second stability legislation. the entire fabric supplied during this booklet is extremely proper for the knowledge of well-balanced schemes and may give a contribution to destiny improvements.
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