Combined Methods for Elliptic Equations with Singularities, Interfaces and Infinities

  • Zi Cai Li

Part of the Mathematics and Its Applications book series (MAIA, volume 444)

Table of contents

  1. Front Matter
    Pages i-xxiv
  2. Singularities, Treatments and Combinations

    1. Front Matter
      Pages 1-1
    2. Zi Cai Li
      Pages 5-48
    3. Zi Cai Li
      Pages 49-97
  3. Combined Methods

    1. Front Matter
      Pages 99-99
    2. Zi Cai Li
      Pages 103-137
    3. Zi Cai Li
      Pages 139-174
    4. Zi Cai Li
      Pages 175-204
  4. Coupling Techniques

    1. Front Matter
      Pages 205-205
    2. Zi Cai Li
      Pages 225-249
    3. Zi Cai Li
      Pages 251-280
    4. Zi Cai Li
      Pages 281-308
    5. Zi Cai Li
      Pages 309-326
    6. Zi Cai Li
      Pages 327-348
  5. Applications and Advanced Topics

    1. Front Matter
      Pages 349-349
    2. Zi Cai Li
      Pages 353-367
    3. Zi Cai Li
      Pages 369-381
    4. Zi Cai Li
      Pages 383-397
    5. Zi Cai Li
      Pages 399-422

About this book

Introduction

In this book the author sets out to answer two important questions: 1. Which numerical methods may be combined together? 2. How can different numerical methods be matched together? In doing so the author presents a number of useful combinations, for instance, the combination of various FEMs, the combinations of FEM-FDM, REM-FEM, RGM-FDM, etc. The combined methods have many advantages over single methods: high accuracy of solutions, less CPU time, less computer storage, easy coupling with singularities as well as the complicated boundary conditions. Since coupling techniques are essential to combinations, various matching strategies among different methods are carefully discussed. The author provides the matching rules so that optimal convergence, even superconvergence, and optimal stability can be achieved, and also warns of the matching pitfalls to avoid.
Audience: The book is intended for both mathematicians and engineers and may be used as text for advanced students.

Keywords

Approximation finite element method numerical method stability

Authors and affiliations

  • Zi Cai Li
    • 1
  1. 1.Department of Applied MathematicsNational Sun Yat-sen UniversityKaohsiungTaiwan

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4613-3338-8
  • Copyright Information Springer-Verlag US 1998
  • Publisher Name Springer, Boston, MA
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4613-3340-1
  • Online ISBN 978-1-4613-3338-8
  • About this book