Numerical Methods for Nonlinear Partial Differential Equations

  • Sören Bartels

Part of the Springer Series in Computational Mathematics book series (SSCM, volume 47)

Table of contents

  1. Front Matter
    Pages i-x
  2. Sören Bartels
    Pages 1-8
  3. Analytical and Numerical Foundations

    1. Front Matter
      Pages 9-9
    2. Sören Bartels
      Pages 11-44
    3. Sören Bartels
      Pages 45-84
    4. Sören Bartels
      Pages 85-123
  4. Approximation of Classical Formulations

    1. Front Matter
      Pages 125-125
    2. Sören Bartels
      Pages 127-152
    3. Sören Bartels
      Pages 153-182
    4. Sören Bartels
      Pages 183-215
    5. Sören Bartels
      Pages 217-257
  5. Methods for Extended Formulations

    1. Front Matter
      Pages 259-259
    2. Sören Bartels
      Pages 261-295
    3. Sören Bartels
      Pages 297-332
    4. Sören Bartels
      Pages 333-363
  6. Back Matter
    Pages 365-393

About this book

Introduction

The description of many interesting phenomena in science and engineering leads to infinite-dimensional minimization or evolution problems that define nonlinear partial differential equations. While the development and analysis of numerical methods for linear partial differential equations is nearly complete, only few results are available in the case of nonlinear equations. This monograph devises numerical methods for nonlinear model problems arising in the mathematical description of phase transitions, large bending problems, image processing, and inelastic material behavior. For each of these problems the underlying mathematical model is discussed, the essential analytical properties are explained, and the proposed numerical method is rigorously analyzed. The practicality of the algorithms is illustrated by means of short implementations.

Keywords

error estimates finite element method nonlinear partial differential equations numerical algorithms numerical analysis

Authors and affiliations

  • Sören Bartels
    • 1
  1. 1.Abteilung für Angewandte MathematikAlbert-Ludwigs-Universität FreiburgFreiburgGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-13797-1
  • Copyright Information Springer International Publishing Switzerland 2015
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-13796-4
  • Online ISBN 978-3-319-13797-1
  • Series Print ISSN 0179-3632
  • Series Online ISSN 2198-3712
  • About this book