Описание: This introduction to the theory of Sobolev spaces and Hilbert space methods in partial differential equations is geared toward readers of modest mathematical backgrounds. It offers coherent, accessible demonstrations of the use of these techniques in developing the foundations of the theory of finite element approximations. J. T. Oden is Director of the Institute for Computational Engineering & Sciences (ICES) at the University of Texas at Austin, and J. N. Reddy is a Professor of Engineering at Texas A&M University. They developed this essentially self-contained text from their seminars and courses for students with diverse educational backgrounds. Their effective presentation begins with introductory accounts of the theory of distributions, Sobolev spaces, intermediate spaces and duality, the theory of elliptic equations, and variational boundary value problems. The second half of the text explores the theory of finite element interpolation, finite element methods for elliptic equations, and finite element methods for initial boundary value problems. Detailed proofs of the major theorems appear throughout the text, in addition to numerous examples.
Описание: Discrepancies frequently occur between a physical system's responses and predictions obtained from mathematical models. The Spectral Stochastic Finite Element Method (SSFEM) has proven successful at forecasting a variety of uncertainties in calculating system responses. This text analyzes a class of discrete mathematical models of engineering systems, identifying key issues and reviewing relevant theoretical concepts, with particular attention to a spectral approach. Random system parameters are modeled as second-order stochastic processes, defined by their mean and covariance functions. Relying on the spectral properties of the covariance function, the Karhunen-Loeve expansion is employed to represent these processes in terms of a countable set of uncorrected random variables, casting the problem in a finite dimensional setting. Various spectral approximations for the stochastic response of the system are obtained. Implementing the concept of generalized inverse leads to an explicit expression for the response process as a multivariate polynomial functional of a set of uncorrelated random variables. Alternatively, the solution process is treated as an element in the Hilbert space of random functions, in which a spectral representation is identified in terms of polynomial chaos. In this context, the solution process is approximated by its projection onto a finite subspace spanned by these polynomials.
Автор: Oden J. Название: Finite Elements of Nonlinear Continua ISBN: 0486449734 ISBN-13(EAN): 9780486449739 Издательство: Amazon Internet Рейтинг: Цена: 6468 р. Наличие на складе: Невозможна поставка.
Описание: This text extends applications of the finite element method from linear problems in elastic structures to a broad class of practical, nonlinear problems in continuum mechanics. Its general and unified treatment of theory and applications emphasizes nonlinear problems in finite elasticity, viscoelasticity, heat conduction, and thermoviscoelasticity. 1972 edition.
Автор: Zienkiewicz, O. Название: Finite Elements and Approximation ISBN: 0486788695 ISBN-13(EAN): 9780486788692 Издательство: Dover Цена: 3340 р. Наличие на складе: Поставка под заказ.
Описание: A powerful tool for the approximate solution of differential equations, the finite element is extensively used in industry and research. This book offers students of engineering and physics a comprehensive view of the principles involved, with numerous illustrative examples and exercises. Starting with continuum boundary value problems and the need for numerical discretization, the text examines finite difference methods, weighted residual methods in the context of continuous trial functions, and piecewise defined trial functions and the finite element method. Additional topics include higher order finite element approximation, mapping and numerical integration, variational methods, and partial discretization and time-dependent problems. A survey of generalized finite elements and error estimates concludes the text.
Автор: Davis, Philip J. Название: Interpolation and Approximation ISBN: 0486624951 ISBN-13(EAN): 9780486624952 Издательство: Dover Рейтинг: Цена: 1919 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Interpolation and approximation offer important applications in computer science and elsewhere. This intermediate-level survey by a noted authority abounds in useful examples of related subjects and has been praised for its level of clarity and reliance on well-presented and useful examples. A brief introductory chapter presents helpful definitions and theorems. Subsequent chapters explore interpolation, remainder theory, convergence theorems for interpolatory processes, and some problems of infinite interpolation. Additional topics include uniform and best approximation, least square approximation, Hilbert space, orthogonal polynomials, the theory of closure and completeness, expansion theorems for orthogonal functions, degree of approximation, and approximation of linear functionals. A familiarity with real and complex variable theory and linear algebra is assumed. 1963 edition.
Описание: This graduate-level text offers a concise butwide-ranging introduction to methods of approximating continuous functions by functions depending only on a finite number of parameters. It places particular emphasis on approximation by polynomials andnot only discusses the theoretical underpinnings of many common algorithms but also demonstrates their practical applications. 1969 edition."
Автор: Achieser N. I. Название: Theory of Approximation ISBN: 0486495434 ISBN-13(EAN): 9780486495439 Издательство: Dover Рейтинг: Цена: 4180 р. Наличие на складе: Поставка под заказ.
Описание: A marriage of the finite-differences method with variational methods for solving boundary-value problems, the finite-element method is superior in many ways to finite-differences alone. This self-contained text for advanced undergraduates and graduate students is intended to imbed this combination of methods into the framework of functional analysis. 1980 edition.
Автор: Niven Ivan Название: Diophantine Approximations ISBN: 0486462676 ISBN-13(EAN): 9780486462677 Издательство: Dover Рейтинг: Цена: 665 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This self-contained treatment covers basic results on homogeneous approximation of real numbers; the analogue for complex numbers; basic results for nonhomogeneous approximation in the real case; the analogue for complex numbers; and fundamental properties of the multiples of an irrational number, for both fractional and integral parts. 1963 edition.
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