Numerical methods for conservation laws

Numerical methods for conservation laws: from analysis to algorithms

by Hesthaven, Jan S

Type Book
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Conservation laws are the mathematical expression of the principles of conservation and provide effective and accurate predictive models of our physical world. Although intense research activity during the last decades has led to substantial advances in the development of powerful computational methods for conservation laws, their solution remains a challenge and many questions are left open; thus it is an active and fruitful area of research. Numerical Methods for Conservation Laws: From Analy…

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Title Statements

  • Full title :Numerical methods for conservation laws : from analysis to algorithms / Jan S. Hesthaven, EPFL, Lausanne, Switzerland.

Summary

Conservation laws are the mathematical expression of the principles of conservation and provide effective and accurate predictive models of our physical world. Although intense research activity during the last decades has led to substantial advances in the development of powerful computational methods for conservation laws, their solution remains a challenge and many questions are left open; thus it is an active and fruitful area of research. Numerical Methods for Conservation Laws: From Analysis to Algorithms offers the first comprehensive introduction to modern computational methods and their analysis for hyperbolic conservation laws, building on intense research activities for more than four decades of development; discusses classic results on monotone and finite difference/finite volume schemes, but emphasizes the successful development of high-order accurate methods for hyperbolic conservation laws; addresses modern concepts of TVD and entropy stability, strongly stable Runge-Kutta schemes, and limiter-based methods before discussing essentially nonoscillatory schemes, discontinuous Galerkin methods, and spectral methods; explores algorithmic aspects of these methods, emphasizing one- and two-dimensional problems and the development and analysis of an extensive range of methods; includes MATLAB software with which all main methods and computational results in the book can be reproduced; and demonstrates the performance of many methods on a set of benchmark problems to allow direct comparisons. Code and other supplemental material will be available online at publication.

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Edition Statements

  • Publication Date:2017

Publication Statements

Notes

Titre de l'écran-titre (visionné en 2019).

In SIAM e-books.

The Physical Object

  • Description:1 ressource en ligne (xvi, 570 pages) : : fichiers PDF.

Edition Identifiers

  • ISBN:9781611975109, 1611975107
  • oclc:on1132100156
  • LC Classification:QC793.3.C58
  • Dewey Decimal:518/.64

Table of Contents

1. Introduction -- part I. Conservation laws -- 2. Scalar conservation laws -- 3. Systems of conservation laws -- part II. Monotone schemes -- 4. From continuous to discrete -- 5. Finite difference methods -- 6. Finite volume methods -- 7. Beyond one dimension -- part III. High-order schemes -- 8. High-order accuracy and its challenges -- 9. Strong stability preserving time integration -- 10. High-order accurate limiter-based methods -- 11. Essentially nonoscillatory schemes -- 12. Discontinuous Galerkin methods -- 13. Spectral methods.

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Subjects

Conservation laws (Physics) Lois de conservation (Physique)

Writers

Hesthaven, Jan S

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