BOUNDARY ELEMENT METHODS WITH APPLICATIONS TO NONLINEAR PROBLEMS

1. Front Matter

   Pages i-xxvi

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2. Introduction

   • Goong Chen, Goong Chen, Jianxin Zhou

   Pages 1-15

3. Some Basic Properties of Sobolev Spaces

   • Goong Chen, Goong Chen, Jianxin Zhou

   Pages 17-31

4. Theory of Distributions

   • Goong Chen, Goong Chen, Jianxin Zhou

   Pages 33-61

5. Pseudodifferential Operators and Their Fredholm Properties

   • Goong Chen, Goong Chen, Jianxin Zhou

   Pages 63-122

6. Finite-Element Methods: Spaces and Properties

   • Goong Chen, Goong Chen, Jianxin Zhou

   Pages 123-189

7. The Potential Equation

   • Goong Chen, Goong Chen, Jianxin Zhou

   Pages 191-300

8. The Helmholtz Equation

   • Goong Chen, Goong Chen, Jianxin Zhou

   Pages 301-372

9. The Thin Plate Equation

   • Goong Chen, Goong Chen, Jianxin Zhou

   Pages 373-439

10. Linear Elastostatics

    • Goong Chen, Goong Chen, Jianxin Zhou

    Pages 441-505

11. Some Error Estimates for Numerical Solutions of Boundary Integral Equations

    • Goong Chen, Goong Chen, Jianxin Zhou

    Pages 507-544

12. Boundary Element Methods for Semilinear Elliptic Partial Differential Equations (I): The Monotone Iteration Scheme and Error Estimates

    • Goong Chen, Goong Chen, Jianxin Zhou

    Pages 545-612

13. Boundary Element Methods for Semilinear Elliptic Partial Differential Equations (II): Algorithms and Computations for Unstable Solutions from Various Models

    • Goong Chen, Goong Chen, Jianxin Zhou

    Pages 613-691

14. Back Matter

    Pages 693-715

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Boundary Element Methods have become a major numerical tool in scientific and engineering problem-solving, with particular applications to numerical computations and simulations of partial differential equations in engineering. Boundary Element Methods provides a rigorous and systematic account of the modern mathematical theory of Boundary Element Methods, including the requisite background on general partial, differential equation methods, Sobolev spaces, pseudo-differential and Fredholm operators and finite elements. It aims at the computation of many types of elliptic boundary value problems in potential theory, elasticity, wave propagation, and structural mechanics. Also presented are various methods and algorithms for nonlinear partial differential equations. This second edition has been fully revised and combines the mathematical rigour necessary for a full understanding of the subject, with extensive examples of applications illustrated with computer graphics. This book is intended as a textbook and reference for applied mathematicians, physical scientists and engineers at graduate and research level. It will be an invaluable sourcebook for all concerned with numerical modeling and the solution of partial differential equations.

• distribution
• engineering
• finite element method
• mathematics
• science

• Mathematics and Aerospace Engineering, Texas A&M University, College Station, USA

  Goong Chen

• Mathematics National Taiwan University, Taipei, Republic of China

  Goong Chen

• Texas A&M University, College Station, USA

  Jianxin Zhou

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