Adaptive Moving Mesh Methods

  • Weizhang Huang
  • Robert D. Russell

Part of the Applied Mathematical Sciences book series (AMS, volume 174)

Table of contents

  1. Front Matter
    Pages i-xvii
  2. Weizhang Huang, Robert D. Russell
    Pages 1-25
  3. Weizhang Huang, Robert D. Russell
    Pages 27-135
  4. Weizhang Huang, Robert D. Russell
    Pages 137-176
  5. Weizhang Huang, Robert D. Russell
    Pages 177-213
  6. Weizhang Huang, Robert D. Russell
    Pages 215-280
  7. Weizhang Huang, Robert D. Russell
    Pages 281-378
  8. Weizhang Huang, Robert D. Russell
    Pages 379-399
  9. Back Matter
    Pages 401-432

About this book

Introduction

Moving mesh methods are an effective, mesh-adaptation-based approach for the numerical solution of mathematical models of physical phenomena. Currently there exist three main strategies for mesh adaptation, namely, to use mesh subdivision,  local high order approximation (sometimes combined with mesh subdivision), and mesh movement. The latter type of adaptive mesh method has been less well studied, both computationally and theoretically.

This book is about adaptive mesh generation and moving mesh methods for the numerical solution of time-dependent partial differential equations. It presents a general framework and theory for adaptive mesh generation and gives a comprehensive treatment of moving mesh methods and their basic components, along with their application for a number of nontrivial physical problems.  Many explicit examples with computed figures illustrate the various methods and the effects of parameter choices for those methods. The partial differential equations considered are mainly parabolic (diffusion-dominated, rather  than convection-dominated).

The extensive bibliography provides an invaluable guide to the literature in this field. Each chapter contains useful exercises. Graduate students, researchers and practitioners working in this area will benefit from this book.

Weizhang Huang is a Professor in the Department of Mathematics at the University of Kansas.

Robert D. Russell is a Professor in the Department of Mathematics at Simon Fraser University.

Keywords

finite difference methods mesh generation monitor functions partial differential equations r-adaptive method

Authors and affiliations

  • Weizhang Huang
    • 1
  • Robert D. Russell
    • 2
  1. 1., Department of MathematicsUniversity of KansasLawrenceUSA
  2. 2.Department of MathematicsSimon Fraser UniversityBurnabyCanada

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4419-7916-2
  • Copyright Information Springer Science+Business Media, LLC 2011
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-4419-7915-5
  • Online ISBN 978-1-4419-7916-2
  • Series Print ISSN 0066-5452
  • About this book
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