ich Olaf Steinbach
Numerical Approximation Methods for Elliptic Boundary Value Problems.
Finite and Boundary Elements.

Springer, New York, 390p., 2008.
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Although the aim of this book is to give a unified introduction into finite and
boundary element methods, the main focus is on the numerical analysis of
boundary integral and boundary element methods.
Starting from the variational formulation of elliptic boundary value problems
boundary integral operators and associated boundary integral equations are
introduced and analyzed. By using finite and boundary elements corresponding
numerical approximation schemes are considered.
This textbook may serve as a basis for an introductory course in particular for
boundary element methods including modern trends such as fast boundary element
methods and efficient solution methods, as well as the coupling of finite and
boundary element methods.

  1. Boundary Value Problems
  2. Function Spaces
  3. Variational Methods
  4. Variational Formulations of Boundary Value Problems
  5. Fundamental Solutions
  6. Boundary Integral Operators
  7. Boundary Integral Equations
  8. Approximation Methods
  9. Finite Elements
  10. Boundary Elements
  11. Finite Element Methods
  12. Boundary Element Methods
  13. Iterative Solution Methods
  14. Fast Boundary Element Methods
  15. Domain Decomposition Methods