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Titlebook: Numerical Approximation Methods for Elliptic Boundary Value Problems; Finite and Boundary Olaf Steinbach Textbook 2008 Springer-Verlag New

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书目名称Numerical Approximation Methods for Elliptic Boundary Value Problems
副标题Finite and Boundary
编辑Olaf Steinbach
视频video
概述Empahises boundary-element methods for which there are few books.Suitable for self study.Exercises included
图书封面Titlebook: Numerical Approximation Methods for Elliptic Boundary Value Problems; Finite and Boundary  Olaf Steinbach Textbook 2008 Springer-Verlag New
描述.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..
出版日期Textbook 2008
关键词Approximation; Boundary; Elliptic; Methods; Numerical; finite element method; numerical methods; operator; p
版次1
doihttps://doi.org/10.1007/978-0-387-68805-3
isbn_softcover978-1-4419-2173-4
isbn_ebook978-0-387-68805-3
copyrightSpringer-Verlag New York 2008
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Function Spaces,In this chapter we introduce the most important function spaces as needed for the weak formulation of boundary value problems. For a further reading we refer to [1, 103, 106].
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Approximation Methods,In this chapter we describe and analyze approximation methods to solve the variational problems for operator equations as formulated in Chapter 3. This is done by introducing conforming finite dimensional trial spaces leading to linear systems of algebraic equations.
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Variational Methods,solutions of partial differential equations by using surface and volume potentials requires the solution of boundary integral operator equations to find the complete Cauchy data. In this chapter we describe the basic tools from functional analysis which are needed to investigate the unique solvability of operator equations.
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Finite Element Methods,ted in Chapter 9. Here we will just consider finite elements of lowest order, in particular we will use piecewise linear and continuous basis functions. The stability and error analysis is imbedded in the general theory as given in Chapter 8. Some numerical examples illustrate the theoretical results.
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