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Approximation and Stability Properties of Numerical Methods for Hyperbolic Conservation Laws

  • Book
  • © 2023

Overview

Authors:
  1. Philipp Öffner

    1. Bremen, Germany

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Table of contents (12 chapters)

  1. Front Matter

    Pages i-xv
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  2. Introduction

    • Philipp Öffner
    Pages 1-6

  3. Foundations of Hyperbolic Problems and Numerical Methods

    1. Front Matter

      Pages 7-7
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    2. Hyperbolic Conservation Laws

      • Philipp Öffner
      Pages 9-34

    3. Numerical Schemes for Hyperbolic Problems

      • Philipp Öffner
      Pages 35-131

  4. Recent Progresses

    1. Front Matter

      Pages 133-133
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    2. Long-time Error Behavior of Discontinuous Galerkin and Flux Reconstruction

      • Philipp Öffner
      Pages 135-193

    3. Uncertainty Quantification for Burgers’ Equation

      • Philipp Öffner
      Pages 195-229

    4. Artificial Viscosity for SBP-FR Methods and the Construction of Fully Discrete Stable Schemes

      • Philipp Öffner
      Pages 231-275

    5. New Stable Discontinuous Galerkin Methods on Equidistant and Scattered Points

      • Philipp Öffner
      Pages 277-298

    6. Construction of Entropy Conservative Flux Reconstruction Schemes on Arbitrary Meshes

      • Philipp Öffner
      Pages 299-314

    7. Analysis, Re-interpretation and Extension of Entropy Correction Terms

      • Philipp Öffner
      Pages 315-339

    8. Analysis of SBP-SAT Stabilisation for Finite Element Methods

      • Philipp Öffner
      Pages 341-379

    9. Arbitrary High-order, Conservative and Positivity Preserving Patankar-type Deferred Correction Schemes

      • Philipp Öffner
      Pages 381-409

    10. Summary & Outlook

      • Philipp Öffner
      Pages 411-413

  5. Back Matter

    Pages 415-483
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Keywords

About this book

The book focuses on stability and approximation results concerning recent numerical methods for the numerical solution of hyperbolic conservation laws. The work begins with a detailed and thorough introduction of hyperbolic conservation/balance laws and their numerical treatment. In the main part, recent results in such context are presented focusing on the investigation of approximation properties of discontinuous Galerkin and flux reconstruction methods, the construction of (entropy) stable numerical methods and the extension of existing (entropy) stability results for both semidiscrete and fully discrete schemes, and development of new high-order methods.

Authors and Affiliations

  • Bremen, Germany

    Philipp Öffner

About the author



About the author
Philipp Öffner is a research associate in the numerical mathematics group at Johannes Gutenberg University Mainz. In his research he focuses on numerical methods for partial differential equations and on scientific computing.

Bibliographic Information

  • Book Title: Approximation and Stability Properties of Numerical Methods for Hyperbolic Conservation Laws

  • Authors: Philipp Öffner

  • DOI: https://doi.org/10.1007/978-3-658-42620-0

  • Publisher: Springer Spektrum Wiesbaden

  • eBook Packages: Life Science and Basic Disciplines (German Language)

  • Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Fachmedien Wiesbaden GmbH, part of Springer Nature 2023

  • Softcover ISBN: 978-3-658-42619-4Published: 17 August 2023

  • eBook ISBN: 978-3-658-42620-0Published: 16 August 2023

  • Edition Number: 1

  • Number of Pages: XV, 486

  • Number of Illustrations: 13 b/w illustrations, 81 illustrations in colour

  • Topics: Computational Mathematics and Numerical Analysis, Applications of Mathematics

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