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Titlebook: Error Estimates for Well-Balanced Schemes on Simple Balance Laws; One-Dimensional Posi Debora Amadori,Laurent Gosse Book 2015 The Author(s)

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书目名称Error Estimates for Well-Balanced Schemes on Simple Balance Laws
副标题One-Dimensional Posi
编辑Debora Amadori,Laurent Gosse
视频videohttp://file.papertrans.cn/315/314923/314923.mp4
概述Surveys both analytical and numerical aspects of 1D hyperbolic balance laws.Presents a strategy for proving the accuracy of well-balanced numerical schemes.Compares several practical schemes, includin
丛书名称SpringerBriefs in Mathematics
图书封面Titlebook: Error Estimates for Well-Balanced Schemes on Simple Balance Laws; One-Dimensional Posi Debora Amadori,Laurent Gosse Book 2015 The Author(s)
描述.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..
出版日期Book 2015
关键词Hyperbolic systems of balance laws; Glimm-Liu-Bressan L1 stability theory; Error estimates for well-ba
版次1
doihttps://doi.org/10.1007/978-3-319-24785-4
isbn_softcover978-3-319-24784-7
isbn_ebook978-3-319-24785-4Series ISSN 2191-8198 Series E-ISSN 2191-8201
issn_series 2191-8198
copyrightThe Author(s) 2015
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https://doi.org/10.1007/978-94-009-4484-8In this chapter we analyze some simple examples, which suggest that the error quantification should take into account of the possible grow in time of the error. This observation provides a motivation for going beyond more classical local-in-time concepts of error (so-called .).
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Sitka Spruce (,, (Bong.) Carr.),In this chapter we illustrate our approach to the error estimate analysis, for a scalar, space-dependent, non-resonant balance law. A wave-front tracking scheme is analyzed, leading to a generic linear dependence in time of the error. Numerical illustrations are given for accretive case and for the case of periodic forcing.
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Cells of the Blood Circulation,In this chapter we address a semilinear system of two equations, in one space dimension, related to the wave equation with space-dependent damping. An approximation scheme is defined, of Well-Balanced type; for this scheme an error estimate is devised by means of the stability analysis for hyperbolic systems.
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Cell and Tissue Reaction EngineeringIn this chapter we analyze the scheme, which was introduced in the previous chapter, by means of a classical Kuznetsov approach. An alternative qualitative estimate, in terms of time and mesh size, is therefore devised. The two estimates are compared, revealing complementary aspects.
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Local and Global Error Estimates,In this chapter we analyze some simple examples, which suggest that the error quantification should take into account of the possible grow in time of the error. This observation provides a motivation for going beyond more classical local-in-time concepts of error (so-called .).
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