An Introduction To The Mathematical Theory Of Finite Elements
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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 Mathematical Theory Of Finite Element Methods
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Author : Susanne Brenner
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
The Mathematical Theory Of Finite Element Methods written by Susanne Brenner 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 2013-03-14 with Mathematics categories.
A rigorous and thorough mathematical introduction to the subject; A clear and concise treatment of modern fast solution techniques such as multigrid and domain decomposition algorithms; Second edition contains two new chapters, as well as many new exercises; Previous edition sold over 3000 copies worldwide
The Mathematical Theory Of Finite Element Methods
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Author : Susanne Brenner
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-12-22
The Mathematical Theory Of Finite Element Methods written by Susanne Brenner 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 is the third and yet further updated edition of a highly regarded mathematical text. Brenner develops the basic mathematical theory of the finite element method, the most widely used technique for engineering design and analysis. Her volume formalizes basic tools that are commonly used by researchers in the field but not previously published. The book is ideal for mathematicians as well as engineers and physical scientists. It can be used for a course that provides an introduction to basic functional analysis, approximation theory, and numerical analysis, while building upon and applying basic techniques of real variable theory. This new edition is substantially updated with additional exercises throughout and new chapters on Additive Schwarz Preconditioners and Adaptive Meshes.
An Introduction To The Mathematical Theory Of Finite Elements
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Author : John Tinsley Oden
language : en
Publisher:
Release Date : 1976
An Introduction To The Mathematical Theory Of Finite Elements written by John Tinsley Oden and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1976 with Approximation theory categories.
Introduction To The Mathematical Theory Of Finite Elements
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Author : JT. ODEN
language : en
Publisher:
Release Date : 1976
Introduction To The Mathematical Theory Of Finite Elements written by JT. ODEN and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1976 with Approximation theory categories.
Mathematical Theory Of Finite Elements
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Author : Leszek F. Demkowicz
language : en
Publisher: SIAM
Release Date : 2023-09-22
Mathematical Theory Of Finite Elements written by Leszek F. Demkowicz and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-09-22 with Mathematics categories.
This book discusses the foundations of the mathematical theory of finite element methods. The focus is on two subjects: the concept of discrete stability, and the theory of conforming elements forming the exact sequence. Both coercive and noncoercive problems are discussed.. Following the historical path of development, the author covers the Ritz and Galerkin methods to Mikhlin’s theory, followed by the Lax–Milgram theorem and Cea’s lemma to the Babuska theorem and Brezzi’s theory. He finishes with an introduction to the discontinuous Petrov–Galerkin (DPG) method with optimal test functions. Based on the author’s personal lecture notes for a popular version of his graduate course on mathematical theory of finite elements, the book includes a unique exposition of the concept of discrete stability and the means to guarantee it, a coherent presentation of finite elements forming the exact grad-curl-div sequence, and an introduction to the DPG method. Intended for graduate students in computational science, engineering, and mathematics programs, Mathematical Theory of Finite Elements is also appropriate for graduate mathematics and mathematically oriented engineering students. Instructors will find the book useful for courses in real analysis, functional analysis, energy (Sobolev) spaces, and Hilbert space methods for PDEs.
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 Elements
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Author : Ivo Babuska
language : en
Publisher: Oxford University Press
Release Date : 2010-11-04
Finite Elements written by Ivo Babuska and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-11-04 with Mathematics categories.
Most of the many books on finite elements are devoted either to mathematical theory or to engineering applications, but not to both. This book presents computed numbers which not only illustrate the theory but can only be analysed using the theory. This approach, both dual and interacting between theory and computation makes this book unique.
An Introduction To Linear And Nonlinear Finite Element Analysis
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Author : Prem Kythe
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-06-27
An Introduction To Linear And Nonlinear Finite Element Analysis written by Prem Kythe 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 2011-06-27 with Mathematics categories.
Modern finite element analysis has grown into a basic mathematical tool for almost every field of engineering and the applied sciences. This introductory textbook fills a gap in the literature, offering a concise, integrated presentation of methods, applications, software tools, and hands-on projects. Included are numerous exercises, problems, and Mathematica/Matlab-based programming projects. The emphasis is on interdisciplinary applications to serve a broad audience of advanced undergraduate/graduate students with different backgrounds in applied mathematics, engineering, physics/geophysics. The work may also serve as a self-study reference for researchers and practitioners seeking a quick introduction to the subject for their research.
Theory And Practice Of Finite Elements
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Author : Alexandre Ern
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
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 2013-03-09 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.