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Field name	Details
Dewey Class	515.353
Title	Nonlinear Stability of Finite Volume Methods for Hyperbolic Conservation Laws ([EBook] /) / by François Bouchut.
Author	Bouchut, François
Other name(s)	SpringerLink (Online service)
Publication	Basel : : Birkhäuser Basel, , 2004.
Physical Details	VIII, 134 p. : online resource.
Series	Frontiers in Mathematics 1660-8046
ISBN	9783764377922
Summary Note	This book is devoted to finite volume methods for hyperbolic systems of conservation laws. It differs from previous expositions on the subject in that the accent is put on the development of tools and the design of schemes for which one can rigorously prove nonlinear stability properties. Sufficient conditions for a scheme to preserve an invariant domain or to satisfy discrete entropy inequalities are systematically exposed, with analysis of suitable CFL conditions. The monograph intends to be a useful guide for the engineer or researcher who needs very practical advice on how to get such desired stability properties. The notion of approximate Riemann solver and the relaxation method, which are adapted to this aim, are especially explained. In particular, practical formulas are provided in a new variant of the HLLC solver for the gas dynamics system, taking care of contact discontinuities, entropy conditions, and including vacuum. In the second half of the book, nonconservative schemes handling source terms are analyzed in the same spirit. The recent developments on well-balanced schemes that are able to capture steady states are explained within a general framework that includes analysis of consistency and order of accuracy. Several schemes are compared for the Saint Venant problem concerning positivity and the ability to treat resonant data. In particular, the powerful and recently developed hydrostatic reconstruction method is detailed.:
Contents note	Introduction -- 1. Quasilinear systems and conservation laws -- 2. Conservative schemes -- 3. Source terms -- 4. Nonconservative schemes -- 5. Multidimensional finite volumes with sources -- 6. Numerical test with source -- Bibliography.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/b93802
Links to Related Works	Subject References: Biomathematics . Classical Continuum Physics . Continuum physics . Mathematical and Computational Biology . Mathematics . Numerical Analysis . Partial differential equations . Authors: Bouchut, François . Corporate Authors: SpringerLink (Online service) . Series: Frontiers in Mathematics . Classification: 515.353 .

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Nonlinear Stability of Finite Volume Methods for Hyperbolic Conservation Laws

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