An Introduction To The Mathematical Theory Of Finite Elements

Author : J. T. Oden,J. N. Reddy
Publisher : Courier Corporation
Page : 450 pages
File Size : 49,5 Mb
Release : 2012-05-23
Category : Technology & Engineering
ISBN : 9780486142210

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An Introduction to the Mathematical Theory of Finite Elements by J. T. Oden,J. N. Reddy Pdf

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.

Author : Susanne Brenner,L. Ridgway Scott
Publisher : Springer Science & Business Media
Page : 369 pages
File Size : 53,9 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9781475736588

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The Mathematical Theory of Finite Element Methods by Susanne Brenner,L. Ridgway Scott Pdf

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

Author : John Tinsley Oden,Junuthula Narasimha Reddy
Publisher : Unknown
Page : 429 pages
File Size : 54,8 Mb
Release : 1976
Category : Approximation theory
ISBN : OCLC:213745870

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An Introduction to the Mathematical Theory of Finite Elements by John Tinsley Oden,Junuthula Narasimha Reddy Pdf

Author : Leszek F. Demkowicz
Publisher : SIAM
Page : 217 pages
File Size : 53,9 Mb
Release : 2023-09-22
Category : Mathematics
ISBN : 9781611977738

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Mathematical Theory of Finite Elements by Leszek F. Demkowicz Pdf

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.

Author : Susanne Brenner,Ridgway Scott
Publisher : Springer Science & Business Media
Page : 403 pages
File Size : 55,5 Mb
Release : 2007-12-14
Category : Mathematics
ISBN : 9780387759333

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The Mathematical Theory of Finite Element Methods by Susanne Brenner,Ridgway Scott Pdf

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.

Author : JT. ODEN,John Tinsley Oden
Publisher : Unknown
Page : 429 pages
File Size : 42,8 Mb
Release : 1976
Category : Approximation theory
ISBN : OCLC:233647442

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Introduction to the Mathematical Theory of Finite Elements by JT. ODEN,John Tinsley Oden Pdf

Author : Mats G. Larson,Fredrik Bengzon
Publisher : Springer Science & Business Media
Page : 403 pages
File Size : 47,6 Mb
Release : 2013-01-13
Category : Computers
ISBN : 9783642332876

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The Finite Element Method: Theory, Implementation, and Applications by Mats G. Larson,Fredrik Bengzon Pdf

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.​

Author : Claes Johnson
Publisher : Courier Corporation
Page : 290 pages
File Size : 41,8 Mb
Release : 2012-05-23
Category : Mathematics
ISBN : 9780486131597

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Numerical Solution of Partial Differential Equations by the Finite Element Method by Claes Johnson Pdf

An accessible introduction to the finite element method for solving numeric problems, this volume offers the keys to an important technique in computational mathematics. Suitable for advanced undergraduate and graduate courses, it outlines clear connections with applications and considers numerous examples from a variety of science- and engineering-related specialties.This text encompasses all varieties of the basic linear partial differential equations, including elliptic, parabolic and hyperbolic problems, as well as stationary and time-dependent problems. Additional topics include finite element methods for integral equations, an introduction to nonlinear problems, and considerations of unique developments of finite element techniques related to parabolic problems, including methods for automatic time step control. The relevant mathematics are expressed in non-technical terms whenever possible, in the interests of keeping the treatment accessible to a majority of students.

Author : Ivo Babuska,John Whiteman,Theofanis Strouboulis
Publisher : Unknown
Page : 336 pages
File Size : 49,6 Mb
Release : 2010-11-04
Category : Mathematics
ISBN : 9780198506690

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Finite Elements by Ivo Babuska,John Whiteman,Theofanis Strouboulis Pdf

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.

Author : Alexandre Ern,Jean-Luc Guermond
Publisher : Springer Science & Business Media
Page : 531 pages
File Size : 44,5 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9781475743555

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Theory and Practice of Finite Elements by Alexandre Ern,Jean-Luc Guermond Pdf

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.

Author : Prem Kythe,Dongming Wei
Publisher : Springer Science & Business Media
Page : 445 pages
File Size : 46,5 Mb
Release : 2011-06-27
Category : Mathematics
ISBN : 9780817681609

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An Introduction to Linear and Nonlinear Finite Element Analysis by Prem Kythe,Dongming Wei Pdf

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.

Author : 3Island Press
Publisher : Unknown
Page : 280 pages
File Size : 53,5 Mb
Release : 1990-01-01
Category : Electronic
ISBN : 3034876319

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Mathematical Theory of Finite and Boundary Element Methods by 3Island Press Pdf

Author : SCI085000
Publisher : SIAM
Page : 186 pages
File Size : 49,5 Mb
Release : 2022-06-27
Category : Mathematics
ISBN : 9781611977097

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Mathematical Foundations of Finite Elements and Iterative Solvers by SCI085000 Pdf

“This book combines an updated look, at an advanced level, of the mathematical theory of the finite element method (including some important recent developments), and a presentation of many of the standard iterative methods for the numerical solution of the linear system of equations that results from finite element discretization, including saddle point problems arising from mixed finite element approximation. For the reader with some prior background in the subject, this text clarifies the importance of the essential ideas and provides a deeper understanding of how the basic concepts fit together.” — Richard S. Falk, Rutgers University “Students of applied mathematics, engineering, and science will welcome this insightful and carefully crafted introduction to the mathematics of finite elements and to algorithms for iterative solvers. Concise, descriptive, and entertaining, the text covers all of the key mathematical ideas and concepts dealing with finite element approximations of problems in mechanics and physics governed by partial differential equations while interweaving basic concepts on Sobolev spaces and basic theorems of functional analysis presented in an effective tutorial style.” — J. Tinsley Oden, The University of Texas at Austin This textbook describes the mathematical principles of the finite element method, a technique that turns a (linear) partial differential equation into a discrete linear system, often amenable to fast linear algebra. Reflecting the author’s decade of experience in the field, Mathematical Foundations of Finite Elements and Iterative Solvers examines the crucial interplay between analysis, discretization, and computations in modern numerical analysis; furthermore, it recounts historical developments leading to current state-of-the-art techniques. While self-contained, this textbook provides a clear and in-depth discussion of several topics, including elliptic problems, continuous Galerkin methods, iterative solvers, advection-diffusion problems, and saddle point problems. Accessible to readers with a beginning background in functional analysis and linear algebra, this text can be used in graduate-level courses on advanced numerical analysis, data science, numerical optimization, and approximation theory. Professionals in numerical analysis and finite element methods will also find the book of interest.

Author : Kendall Atkinson,Weimin Han
Publisher : Springer Science & Business Media
Page : 576 pages
File Size : 45,6 Mb
Release : 2007-06-07
Category : Mathematics
ISBN : 9780387287690

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Theoretical Numerical Analysis by Kendall Atkinson,Weimin Han Pdf

Mathematics is playing an ever more important role in the physical and biological sciences, provoking a blurring of boundaries between scienti?c disciplines and a resurgence of interest in the modern as well as the cl- sical techniques of applied mathematics. This renewal of interest, both in research and teaching, has led to the establishment of the series: Texts in Applied Mathematics (TAM). Thedevelopmentofnewcoursesisanaturalconsequenceofahighlevelof excitement on the research frontier as newer techniques, such as numerical and symbolic computer systems, dynamical systems, and chaos, mix with and reinforce the traditional methods of applied mathematics. Thus, the purpose of this textbook series is to meet the current and future needs of these advances and to encourage the teaching of new courses. TAM will publish textbooks suitable for use in advanced undergraduate and beginning graduate courses, and will complement the Applied Ma- ematical Sciences (AMS) series, which will focus on advanced textbooks and research-level monographs.

Author : Sandeep Kumar,Ashish Pathak,Debashis Khan
Publisher : CRC Press
Page : 230 pages
File Size : 48,7 Mb
Release : 2019-07-09
Category : Mathematics
ISBN : 9781351685443

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Mathematical Theory of Subdivision by Sandeep Kumar,Ashish Pathak,Debashis Khan Pdf

This book provides good coverage of the powerful numerical techniques namely, finite element and wavelets, for the solution of partial differential equation to the scientists and engineers with a modest mathematical background. The objective of the book is to provide the necessary mathematical foundation for the advanced level applications of these numerical techniques. The book begins with the description of the steps involved in finite element and wavelets-Galerkin methods. The knowledge of Hilbert and Sobolev spaces is needed to understand the theory of finite element and wavelet-based methods. Therefore, an overview of essential content such as vector spaces, norm, inner product, linear operators, spectral theory, dual space, and distribution theory, etc. with relevant theorems are presented in a coherent and accessible manner. For the graduate students and researchers with diverse educational background, the authors have focused on the applications of numerical techniques which are developed in the last few decades. This includes the wavelet-Galerkin method, lifting scheme, and error estimation technique, etc. Features: • Computer programs in Mathematica/Matlab are incorporated for easy understanding of wavelets. • Presents a range of workout examples for better comprehension of spaces and operators. • Algorithms are presented to facilitate computer programming. • Contains the error estimation techniques necessary for adaptive finite element method. This book is structured to transform in step by step manner the students without any knowledge of finite element, wavelet and functional analysis to the students of strong theoretical understanding who will be ready to take many challenging research problems in this area.