Finite Elements And Approximation

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Finite Elements And Approximation

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Author : O. C. Zienkiewicz
language : en
Publisher: Courier Corporation
Release Date : 2006-01-01

Finite Elements And Approximation written by O. C. Zienkiewicz and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-01-01 with Technology & Engineering categories.

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.

The Finite Element Method For Boundary Value Problems

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Author : Karan S. Surana
language : en
Publisher: CRC Press
Release Date : 2016-11-17

The Finite Element Method For Boundary Value Problems written by Karan S. Surana and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-11-17 with Science categories.

Written by two well-respected experts in the field, The Finite Element Method for Boundary Value Problems: Mathematics and Computations bridges the gap between applied mathematics and application-oriented computational studies using FEM. Mathematically rigorous, the FEM is presented as a method of approximation for differential operators that are mathematically classified as self-adjoint, non-self-adjoint, and non-linear, thus addressing totality of all BVPs in various areas of engineering, applied mathematics, and physical sciences. These classes of operators are utilized in various methods of approximation: Galerkin method, Petrov-Galerkin Method, weighted residual method, Galerkin method with weak form, least squares method based on residual functional, etc. to establish unconditionally stable finite element computational processes using calculus of variations. Readers are able to grasp the mathematical foundation of finite element method as well as its versatility of applications. h-, p-, and k-versions of finite element method, hierarchical approximations, convergence, error estimation, error computation, and adaptivity are additional significant aspects of this book.

An Introduction To The Mathematical Theory Of Finite Elements

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Author : J. T. Oden
language : en
Publisher: Courier Corporation
Release Date : 2012-05-23

An Introduction To The Mathematical Theory Of Finite Elements written by J. T. Oden and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-05-23 with Technology & Engineering categories.

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.

The Finite Element Method For Elliptic Problems

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Author : P.G. Ciarlet
language : en
Publisher: Elsevier
Release Date : 1978-01-01

The Finite Element Method For Elliptic Problems written by P.G. Ciarlet and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1978-01-01 with Mathematics categories.

The objective of this book is to analyze within reasonable limits (it is not a treatise) the basic mathematical aspects of the finite element method. The book should also serve as an introduction to current research on this subject. On the one hand, it is also intended to be a working textbook for advanced courses in Numerical Analysis, as typically taught in graduate courses in American and French universities. For example, it is the author's experience that a one-semester course (on a three-hour per week basis) can be taught from Chapters 1, 2 and 3 (with the exception of Section 3.3), while another one-semester course can be taught from Chapters 4 and 6. On the other hand, it is hoped that this book will prove to be useful for researchers interested in advanced aspects of the numerical analysis of the finite element method. In this respect, Section 3.3, Chapters 5, 7 and 8, and the sections on "Additional Bibliography and Comments should provide many suggestions for conducting seminars.

The Finite Element Method Set

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Author : O. C. Zienkiewicz
language : en
Publisher: Elsevier
Release Date : 2005-11-25

The Finite Element Method Set written by O. C. Zienkiewicz and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-11-25 with Technology & Engineering categories.

The sixth editions of these seminal books deliver the most up to date and comprehensive reference yet on the finite element method for all engineers and mathematicians. Renowned for their scope, range and authority, the new editions have been significantly developed in terms of both contents and scope. Each book is now complete in its own right and provides self-contained reference; used together they provide a formidable resource covering the theory and the application of the universally used FEM. Written by the leading professors in their fields, the three books cover the basis of the method, its application to solid mechanics and to fluid dynamics.* This is THE classic finite element method set, by two the subject's leading authors * FEM is a constantly developing subject, and any professional or student of engineering involved in understanding the computational modelling of physical systems will inevitably use the techniques in these books * Fully up-to-date; ideal for teaching and reference

Numerical Approximation Methods For Elliptic Boundary Value Problems

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Author : Olaf Steinbach
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-12-22

Numerical Approximation Methods For Elliptic Boundary Value Problems written by Olaf Steinbach and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-12-22 with Mathematics categories.

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.

Finite Element Approximation Of The Navier Stokes Equations

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Author : Vivette Girault
language : en
Publisher: Springer
Release Date : 1979

Finite Element Approximation Of The Navier Stokes Equations written by Vivette Girault and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1979 with Finite element method categories.

The Finite Element Method Theory Implementation And Applications

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Author : Mats G. Larson
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-01-13

The Finite Element Method Theory Implementation And Applications written by Mats G. Larson and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-01-13 with Computers categories.

This book gives an introduction to the finite element method as a general computational method for solving partial differential equations approximately. Our approach is mathematical in nature with a strong focus on the underlying mathematical principles, such as approximation properties of piecewise polynomial spaces, and variational formulations of partial differential equations, but with a minimum level of advanced mathematical machinery from functional analysis and partial differential equations. In principle, the material should be accessible to students with only knowledge of calculus of several variables, basic partial differential equations, and linear algebra, as the necessary concepts from more advanced analysis are introduced when needed. Throughout the text we emphasize implementation of the involved algorithms, and have therefore mixed mathematical theory with concrete computer code using the numerical software MATLAB is and its PDE-Toolbox. We have also had the ambition to cover some of the most important applications of finite elements and the basic finite element methods developed for those applications, including diffusion and transport phenomena, solid and fluid mechanics, and also electromagnetics.​

Finite Element Solution Of Boundary Value Problems

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Author : O. Axelsson
language : en
Publisher: SIAM
Release Date : 2001-01-01

Finite Element Solution Of Boundary Value Problems written by O. Axelsson and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-01-01 with Mathematics categories.

a thorough, balanced introduction to both the theoretical and the computational aspects of the topic.

Theory And Practice Of Finite Elements

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Author : Alexandre Ern
language : en
Publisher: Springer Science & Business Media
Release Date : 2004-04-29

Theory And Practice Of Finite Elements written by Alexandre Ern and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-04-29 with Mathematics categories.

This text presenting the mathematical theory of finite elements is organized into three main sections. The first part develops the theoretical basis for the finite element methods, emphasizing inf-sup conditions over the more conventional Lax-Milgrim paradigm. The second and third parts address various applications and practical implementations of the method, respectively. It contains numerous examples and exercises.