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024 7 $a10.1007/978-3-319-24785-4
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035   $a(DE-He213)978-3-319-24785-4
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100   $a20151023d2015      u|             0
101 0 $aeng
135   $aur|n|---|||||
181   $ctxt
182   $cc
183   $acr
200 10$aError estimates for well-balanced schemes on simple balance laws$b[electronic resource] $eone-dimensional position-dependent models /$fby Debora Amadori, Laurent Gosse
205   $a1st ed. 2015.
210  1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2015.
215   $a1 online resource (119 p.)
225 1 $aSpringerBriefs in Mathematics,$x2191-8198
300   $aDescription based upon print version of record.
311   $a3-319-24784-0 
320   $aIncludes bibliographical references at the end of each chapters and index.
327   $a1 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.
330   $aThis monograph presents, in an attractive and self-contained form, techniques based on the L1 stability theory derived at the end of the 1990s by A. Bressan, T.-P. Liu and T. Yang that yield original error estimates for so-called well-balanced numerical schemes solving 1D hyperbolic systems of balance laws. Rigorous error estimates are presented for both scalar balance laws and a position-dependent relaxation system, in inertial approximation. Such estimates shed light on why those algorithms based on source terms handled like "local scatterers" can outperform other, more standard, numerical schemes. Two-dimensional Riemann problems for the linear wave equation are also solved, with discussion of the issues raised relating to the treatment of 2D balance laws. All of the material provided in this book is highly relevant for the understanding of well-balanced schemes and will contribute to future improvements.
410  0$aSpringerBriefs in Mathematics,$x2191-8198
606   $aPartial differential equations
606   $aNumerical analysis
606   $aMathematical physics
606   $aPhysics
606   $aPartial Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12155
606   $aNumerical Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M14050
606   $aMathematical Applications in the Physical Sciences$3https://scigraph.springernature.com/ontologies/product-market-codes/M13120
606   $aNumerical and Computational Physics, Simulation$3https://scigraph.springernature.com/ontologies/product-market-codes/P19021
615  0$aPartial differential equations.
615  0$aNumerical analysis.
615  0$aMathematical physics.
615  0$aPhysics.
615 14$aPartial Differential Equations.
615 24$aNumerical Analysis.
615 24$aMathematical Applications in the Physical Sciences.
615 24$aNumerical and Computational Physics, Simulation.
676   $a515.3535
700   $aAmadori$b Debora$4aut$4http://id.loc.gov/vocabulary/relators/aut$0755676
702   $aGosse$b Laurent$4aut$4http://id.loc.gov/vocabulary/relators/aut
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a9910300250803321
996   $aError Estimates for Well-Balanced Schemes on Simple Balance Laws$92545888
997   $aUNINA