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Wave Phenomena

Mathematical Analysis and Numerical Approximation

  • Textbook
  • © 2023

Overview

Authors:
  1. Willy Dörfler

    1. Institute for Applied and Numerical Mathematics, Karlsruhe Institute of Technology, Karlsruhe, Germany

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  2. Marlis Hochbruck

    1. Institute for Applied and Numerical Mathematics, Karlsruhe Institute of Technology, Karlsruhe, Germany

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  3. Jonas Köhler

    1. Institute for Applied and Numerical Mathematics, Karlsruhe Institute of Technology, Karlsruhe, Germany

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  4. Andreas Rieder

    1. Institute for Applied and Numerical Mathematics, Karlsruhe Institute of Technology, Karlsruhe, Germany

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  5. Roland Schnaubelt

    1. Institute for Analysis, Karlsruhe Institute of Technology, Karlsruhe, Germany

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  6. Christian Wieners

    1. Institute for Applied and Numerical Mathematics, Karlsruhe Institute of Technology, Karlsruhe, Germany

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  • Presents a comprehensive introduction to the research on wave phenomena
  • Intertwines analysis and numerical mathematics for wave-type problems
  • Starts with basic topics

Part of the book series: Oberwolfach Seminars (OWS, volume 49)

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Table of contents (20 chapters)

  1. Front Matter

    Pages i-xiv
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  2. Space-Time Approximations for Linear Acoustic, Elastic, and Electro-Magnetic Wave Equations

    1. Front Matter

      Pages 1-1
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    2. Modeling of Acoustic, Elastic, and Electro-Magnetic Waves

      • Willy Dörfler, Marlis Hochbruck, Jonas Köhler, Andreas Rieder, Roland Schnaubelt, Christian Wieners
      Pages 3-18

    3. Space-Time Solutions for Linear Hyperbolic Systems

      • Willy Dörfler, Marlis Hochbruck, Jonas Köhler, Andreas Rieder, Roland Schnaubelt, Christian Wieners
      Pages 19-34

    4. Discontinuous Galerkin Methods for Linear Hyperbolic Systems

      • Willy Dörfler, Marlis Hochbruck, Jonas Köhler, Andreas Rieder, Roland Schnaubelt, Christian Wieners
      Pages 35-48

    5. A Petrov–Galerkin Space-Time Approximation for Linear Hyperbolic Systems

      • Willy Dörfler, Marlis Hochbruck, Jonas Köhler, Andreas Rieder, Roland Schnaubelt, Christian Wieners
      Pages 49-69

  3. Local Wellposedness and Long-Time Behavior of Quasilinear Maxwell Equations

    1. Front Matter

      Pages 71-71
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    2. Introduction and Local Wellposedness on \(\mathbb {R}^3\)

      • Willy Dörfler, Marlis Hochbruck, Jonas Köhler, Andreas Rieder, Roland Schnaubelt, Christian Wieners
      Pages 73-105

    3. Local Wellposedness on a Domain

      • Willy Dörfler, Marlis Hochbruck, Jonas Köhler, Andreas Rieder, Roland Schnaubelt, Christian Wieners
      Pages 107-131

    4. Exponential Decay Caused by Conductivity

      • Willy Dörfler, Marlis Hochbruck, Jonas Köhler, Andreas Rieder, Roland Schnaubelt, Christian Wieners
      Pages 133-159

  4. Error Analysis of Second-Order Time Integration Methods for Discontinuous Galerkin Discretizations of Friedrichs’ Systems

    1. Front Matter

      Pages 161-161
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    2. Introduction

      • Willy Dörfler, Marlis Hochbruck, Jonas Köhler, Andreas Rieder, Roland Schnaubelt, Christian Wieners
      Pages 163-166

    3. Linear Wave-Type Equations

      • Willy Dörfler, Marlis Hochbruck, Jonas Köhler, Andreas Rieder, Roland Schnaubelt, Christian Wieners
      Pages 167-185

    4. Spatial Discretization

      • Willy Dörfler, Marlis Hochbruck, Jonas Köhler, Andreas Rieder, Roland Schnaubelt, Christian Wieners
      Pages 187-200

    5. Full Discretization

      • Willy Dörfler, Marlis Hochbruck, Jonas Köhler, Andreas Rieder, Roland Schnaubelt, Christian Wieners
      Pages 201-241

    6. Error Analysis

      • Willy Dörfler, Marlis Hochbruck, Jonas Köhler, Andreas Rieder, Roland Schnaubelt, Christian Wieners
      Pages 243-267

    7. Appendix

      • Willy Dörfler, Marlis Hochbruck, Jonas Köhler, Andreas Rieder, Roland Schnaubelt, Christian Wieners
      Pages 269-274

    8. List of Definitions

      • Willy Dörfler, Marlis Hochbruck, Jonas Köhler, Andreas Rieder, Roland Schnaubelt, Christian Wieners
      Pages 275-277

  5. An Abstract Framework for Inverse Wave Problems with Applications

    1. Front Matter

      Pages 279-279
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    2. What Is an Inverse and Ill-Posed Problem?

      • Willy Dörfler, Marlis Hochbruck, Jonas Köhler, Andreas Rieder, Roland Schnaubelt, Christian Wieners
      Pages 281-284
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Keywords

About this book

This book presents the notes from the seminar on wave phenomena given in 2019 at the Mathematical Research Center in Oberwolfach.


The research on wave-type problems is a fascinating and emerging field in mathematical research with many challenging applications in sciences and engineering. Profound investigations on waves require a strong interaction of several mathematical disciplines including functional analysis, partial differential equations, mathematical modeling, mathematical physics, numerical analysis, and scientific computing.

The goal of this book is to present a comprehensive introduction to the research on wave phenomena. Starting with basic models for acoustic, elastic, and electro-magnetic waves, topics such as the existence of solutions for linear and some nonlinear material laws, efficient discretizations and solution methods in space and time, and the application to inverse parameter identification problems are covered. The aim of this book is to intertwine analysis and numerical mathematics for wave-type problems promoting thus cooperative research projects in this field.

Authors and Affiliations

  • Institute for Applied and Numerical Mathematics, Karlsruhe Institute of Technology, Karlsruhe, Germany

    Willy Dörfler, Marlis Hochbruck, Jonas Köhler, Andreas Rieder, Christian Wieners

  • Institute for Analysis, Karlsruhe Institute of Technology, Karlsruhe, Germany

    Roland Schnaubelt

About the authors

All authors are teaching and researching at Karlsruhe Institute of Technology, Germany.

Bibliographic Information

  • Book Title: Wave Phenomena

  • Book Subtitle: Mathematical Analysis and Numerical Approximation

  • Authors: Willy Dörfler, Marlis Hochbruck, Jonas Köhler, Andreas Rieder, Roland Schnaubelt, Christian Wieners

  • Series Title: Oberwolfach Seminars

  • DOI: https://doi.org/10.1007/978-3-031-05793-9

  • Publisher: Birkhäuser Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2023

  • Softcover ISBN: 978-3-031-05792-2Published: 31 March 2023

  • eBook ISBN: 978-3-031-05793-9Published: 30 March 2023

  • Series ISSN: 1661-237X

  • Series E-ISSN: 2296-5041

  • Edition Number: 1

  • Number of Pages: XIV, 368

  • Number of Illustrations: 1 b/w illustrations

  • Topics: Computational Mathematics and Numerical Analysis, Analysis

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