Combined Methods for Elliptic Equations with Singularities, Interfaces and Infinities

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

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      Pages 5-48

   3. Singularities and Treatments

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      Pages 49-97

3. Combined Methods

   1. Front Matter

      Pages 99-99

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   2. Boundary Approximation Methods

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      Pages 103-137

   3. Combinations of RGM and FEM

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      Pages 139-174

   4. Combinations of Various Fems

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      Pages 175-204

4. Coupling Techniques

   1. Front Matter

      Pages 205-205

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   2. Lagrange Multipliers and Other Coupling Techniques

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      Pages 209-224

   3. Penalty Techniques

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      Pages 225-249

   4. Simplified Hybrid Methods

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      Pages 251-280

   5. Penalty Plus Hybrid Techniques

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      Pages 281-308

   6. Optimal Combinations for Various Fems

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      Pages 309-326

   7. Combinations of RGM and FDM

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      Pages 327-348

5. Applications and Advanced Topics

   1. Front Matter

      Pages 349-349

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   2. Crack-Infinity Problem

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      Pages 353-367

   3. Wind Flow Over Buildings

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      Pages 369-381

   4. Global Superconvergence in Combinations

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      Pages 383-397

   5. Iterative Substructing Methods

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      Pages 399-422

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.

• Approximation
• finite element method
• numerical method
• stability

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

  Zi Cai Li

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