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.

Numerical Approximation Methods for Elliptic Boundary Value Problems: Finite and Boundary Elements (Texts in Applied Mathematics)

Science & Math

Steinbach, Olaf

Mathematics

Springer

This book provides a detailed description of fast boundary element methods, all based on rigorous mathematical analysis. In particular, the authors use a symmetric formulation of boundary integral equations as well as discussing Galerkin discretisation. All the necessary related stability and error estimates are derived. The authors therefore describe the Adaptive Cross Approximation Algorithm, starting from the basic ideas and proceeding to their practical realization. Numerous examples representing standard problems are given.

The Fast Solution of Boundary Integral Equations (Mathematical and Analytical Techniques with Applications to Engineering)

Computers & Technology

Rjasanow, Sergej

Computer Science

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. It is one of the first books on Theory of Boundary Element Methods.

Numerical Approximation Methods for Elliptic Boundary Value Problems: Finite and Boundary Elements

This book provides a detailed description of fast boundary element methods, all based on rigorous mathematical analysis. In particular, the authors use a symmetric formulation of boundary integral equations as well as discussing Galerkin discretisation. All the necessary related stability and error estimates are derived. The authors therefore describe the Adaptive Cross Approximation Algorithm, starting from the basic ideas and proceeding to their practical realization. Numerous examples representing standard problems are given.

Diese dreisemestrige Einführung in die Analysis behandelt die Integral- und Differentialrechnung einer und mehrerer Veränderlicher. Daran anschließend werden analytische und einfache numerische Verfahren zur Lösung gewöhnlicher Differentialgleichungen besprochen. Der letzte Teil ist Methoden der komplexen Funktionentheorie gewidmet. Zentrales Anliegen dieses Lehrbuches sind die Entwicklung und Anwendung von praktischen Methoden zur Lösung mathematischer Aufgaben sowie die Konstruktion dieser Lösungen.

Analysis: Integral- und Differentialrechnung, gewöhnliche Differentialgleichungen, komplexe Funktionentheorie (German Edition)

Wendland, Wolfgang L.

Vieweg+Teubner Verlag

Domain decomposition methods are a well established tool for an efficient numerical solution of partial differential equations, in particular for the coupling of different model equations and of different discretization methods. Based on the approximate solution of local boundary value problems either by finite or boundary element methods, the global problem is reduced to an operator equation on the skeleton of the domain decomposition. Different variational formulations then lead to hybrid domain decomposition methods.

Stability Estimates for Hybrid Coupled Domain Decomposition Methods (Lecture Notes in Mathematics, 1809)

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Books by Steinbach, Olaf

See the best price to sell, buy, or rent books by Steinbach, Olaf. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Numerical Approximation Methods for Elliptic Boundary Value Problems: Finite and Boundary Elements (Texts in Applied Mathematics)

The Fast Solution of Boundary Integral Equations (Mathematical and Analytical Techniques with Applications to Engineering)

Numerical Approximation Methods for Elliptic Boundary Value Problems: Finite and Boundary Elements

The Fast Solution of Boundary Integral Equations (Mathematical and Analytical Techniques with Applications to Engineering)

Analysis: Integral- und Differentialrechnung, gewöhnliche Differentialgleichungen, komplexe Funktionentheorie (German Edition)

Stability Estimates for Hybrid Coupled Domain Decomposition Methods (Lecture Notes in Mathematics, 1809)