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Partial Differential Equations: Modeling, Analysis and Numerical Approximation

  • Hervé Le Dret
  • Brigitte Lucquin

Part of the International Series of Numerical Mathematics book series (ISNM, volume 168)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Hervé Le Dret, Brigitte Lucquin
    Pages 1-34
  3. Hervé Le Dret, Brigitte Lucquin
    Pages 35-67
  4. Hervé Le Dret, Brigitte Lucquin
    Pages 69-116
  5. Hervé Le Dret, Brigitte Lucquin
    Pages 117-143
  6. Hervé Le Dret, Brigitte Lucquin
    Pages 145-166
  7. Hervé Le Dret, Brigitte Lucquin
    Pages 167-218
  8. Hervé Le Dret, Brigitte Lucquin
    Pages 219-251
  9. Hervé Le Dret, Brigitte Lucquin
    Pages 253-305
  10. Hervé Le Dret, Brigitte Lucquin
    Pages 307-344
  11. Hervé Le Dret, Brigitte Lucquin
    Pages 345-382
  12. Back Matter
    Pages 383-395

About this book

Introduction

This book is devoted to the study of partial differential equation problems both from the theoretical and numerical points of view. After presenting modeling aspects, it develops the theoretical analysis of partial differential equation problems for the three main classes of partial differential equations: elliptic, parabolic and hyperbolic. Several numerical approximation methods adapted to each of these examples are analyzed: finite difference, finite element and finite volumes methods, and they are illustrated using numerical simulation results. Although parts of the book are accessible to Bachelor students in mathematics or engineering, it is primarily aimed at Masters students in applied mathematics or computational engineering. The emphasis is on mathematical detail and rigor for the analysis of both continuous and discrete problems.

 

Keywords

analysis of partial differential equations numerical analysis numerical approximation methods modeling numerical simulations

Authors and affiliations

  • Hervé Le Dret
    • 1
  • Brigitte Lucquin
    • 2
  1. 1.UPMC Université Paris 06, UMR 7598Sorbonne UniversitésParisFrance
  2. 2.UPMC Université Paris 06, UMR 7598Sorbonne UniversitésParisFrance

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-27067-8
  • Copyright Information Springer International Publishing Switzerland 2016
  • Publisher Name Birkhäuser, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-27065-4
  • Online ISBN 978-3-319-27067-8
  • Series Print ISSN 0373-3149
  • Series Online ISSN 2296-6072
  • Buy this book on publisher's site