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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.
List of contents
Boundary Value Problems.- Function Spaces.- Variational Methods.- Variational Formulations of Boundary Value Problems.- Fundamental Solutions.- Boundary Integral Operators.- Boundary Integral Equations.- Approximation Methods.- Finite Elements.- Boundary Elements.- Finite Element Methods.- Boundary Element Methods.- Iterative Solution Methods.- Fast Boundary Element Methods.- Domain Decomposition Methods.
Summary
This book presents a unified theory of the Finite Element Method and the Boundary Element Method for a numerical solution of second order elliptic boundary value problems. While there are textbooks on the finite element method, this is one of the first books on Theory of Boundary Element Methods. The book includes the solvability, stability, and error analysis as well as efficient methods to solve the resulting linear systems. Applications are the potential equation, the system of linear elastostatics and the Stokes system. The book is suitable for self study and exercises are included.
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From the reviews:
“Steinbach introduces known fundamental solutions … for the potential equation, linear elasticity, the Stokes system, and the Helmholtz equation. … For a reader who has a basic knowledge of functional analysis, Steinbach’s book is a nice and relatively compact introduction to the error analysis of Galerkin boundary element methods and its fast realization.” (Hans-Görg Roos, SIAM Review, Vol. 52 (4), 2010)
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From the reviews:
"Steinbach introduces known fundamental solutions ... for the potential equation, linear elasticity, the Stokes system, and the Helmholtz equation. ... For a reader who has a basic knowledge of functional analysis, Steinbach's book is a nice and relatively compact introduction to the error analysis of Galerkin boundary element methods and its fast realization." (Hans-Görg Roos, SIAM Review, Vol. 52 (4), 2010)
