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Combined Methods for Elliptic Equations with Singularities, Interfaces and Infinities

  • Book
  • © 1998

Overview

Authors:
  1. Zi Cai Li

    1. Department of Applied Mathematics, National Sun Yat-sen University, Kaohsiung, Taiwan

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

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Table of contents (17 chapters)

  1. Front Matter

    Pages i-xxiv
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  2. Singularities, Treatments and Combinations

    1. Front Matter

      Pages 1-1
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    2. Different Numerical Methods

      • Zi Cai Li
      Pages 5-48

    3. Singularities and Treatments

      • Zi Cai Li
      Pages 49-97

  3. Combined Methods

    1. Front Matter

      Pages 99-99
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    2. Boundary Approximation Methods

      • Zi Cai Li
      Pages 103-137

    3. Combinations of RGM and FEM

      • Zi Cai Li
      Pages 139-174

    4. Combinations of Various Fems

      • Zi Cai Li
      Pages 175-204

  4. Coupling Techniques

    1. Front Matter

      Pages 205-205
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    2. Lagrange Multipliers and Other Coupling Techniques

      • Zi Cai Li
      Pages 209-224

    3. Penalty Techniques

      • Zi Cai Li
      Pages 225-249

    4. Simplified Hybrid Methods

      • Zi Cai Li
      Pages 251-280

    5. Penalty Plus Hybrid Techniques

      • Zi Cai Li
      Pages 281-308

    6. Optimal Combinations for Various Fems

      • Zi Cai Li
      Pages 309-326

    7. Combinations of RGM and FDM

      • Zi Cai Li
      Pages 327-348

  5. Applications and Advanced Topics

    1. Front Matter

      Pages 349-349
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    2. Crack-Infinity Problem

      • Zi Cai Li
      Pages 353-367

    3. Wind Flow Over Buildings

      • Zi Cai Li
      Pages 369-381

    4. Global Superconvergence in Combinations

      • Zi Cai Li
      Pages 383-397

    5. Iterative Substructing Methods

      • Zi Cai Li
      Pages 399-422
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Keywords

About this book

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.

Authors and Affiliations

  • Department of Applied Mathematics, National Sun Yat-sen University, Kaohsiung, Taiwan

    Zi Cai Li

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