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Numerical Approximation Methods for Elliptic Boundary Value Problems: Finite and Boundary Elements (Texts in Applied Mathematics) - Hardcover
Synopsis
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. This 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. While there are textbooks on the finite element method, this is one of the first books on Theory of Boundary Element Methods. It is suitable for self study and exercises are included.
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From the Back Cover
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.
Review
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)"About this title" may belong to another edition of this title.
- PublisherSpringer
- Publication date2007
- ISBN 10 0387313125
- ISBN 13 9780387313122
- BindingHardcover
- LanguageEnglish
- Number of pages398
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