The Mathematical Foundations Of The Finite Element Method With Applications To Partial Differential Equations

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The Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations

A. K. Aziz
The Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations Book PDF

Author : A. K. Aziz
Publisher : Academic Press
Page : 796 pages
File Size : 45,6 Mb
Release : 2014-05-10
Category : Technology & Engineering
ISBN : 9781483267982

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The Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations by A. K. Aziz Pdf

The Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations is a collection of papers presented at the 1972 Symposium by the same title, held at the University of Maryland, Baltimore County Campus. This symposium relates considerable numerical analysis involved in research in both theoretical and practical aspects of the finite element method. This text is organized into three parts encompassing 34 chapters. Part I focuses on the mathematical foundations of the finite element method, including papers on theory of approximation, variational principles, the problems of perturbations, and the eigenvalue problem. Part II covers a large number of important results of both a theoretical and a practical nature. This part discusses the piecewise analytic interpolation and approximation of triangulated polygons; the Patch test for convergence of finite elements; solutions for Dirichlet problems; variational crimes in the field; and superconvergence result for the approximate solution of the heat equation by a collocation method. Part III explores the many practical aspects of finite element method. This book will be of great value to mathematicians, engineers, and physicists.

Mathematical Foundations of Finite Elements and Iterative Solvers

SCI085000
Mathematical Foundations of Finite Elements and Iterative Solvers Book PDF

Author : SCI085000
Publisher : SIAM
Page : 186 pages
File Size : 53,7 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.

The Finite Element Method: Theory, Implementation, and Applications

Mats G. Larson,Fredrik Bengzon
The Finite Element Method Theory Implementation and Applications Book PDF

Author : Mats G. Larson,Fredrik Bengzon
Publisher : Springer Science & Business Media
Page : 403 pages
File Size : 40,5 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.​

The Mathematical Basis of Finite Element Methods with Applications to Partial Differential Equations

Institute of Mathematics and Its Applications
The Mathematical Basis of Finite Element Methods with Applications to Partial Differential Equations Book PDF

Author : Institute of Mathematics and Its Applications
Publisher : Oxford University Press, USA
Page : 208 pages
File Size : 49,7 Mb
Release : 1984
Category : Differential equations, Partial
ISBN : UCAL:B4527758

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The Mathematical Basis of Finite Element Methods with Applications to Partial Differential Equations by Institute of Mathematics and Its Applications Pdf

Combining theoretical insights with practical applications, this stimulating collection provides a state-of-the-art survey of the finite element method, one of the most powerful tools available for the solution of physical problems. Written by leading experts, this volume consider such topics as parabolic Galerkin methods, nonconforming elements, the treatment of singularities in elliptic boundary value problems, and conforming methods for self-adjount elliptic problems. This will be an invaluable basic reference for computational mathematicians and engineers who use finite element methods in academic or industrial research.

The Finite Element Method and Its Reliability

Ivo Babuška,Theofanis Strouboulis
The Finite Element Method and Its Reliability Book PDF

Author : Ivo Babuška,Theofanis Strouboulis
Publisher : Oxford University Press
Page : 820 pages
File Size : 40,7 Mb
Release : 2001
Category : Mathematics
ISBN : 0198502761

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The Finite Element Method and Its Reliability by Ivo Babuška,Theofanis Strouboulis Pdf

The finite element method is a numerical method widely used in engineering. Experience shows that unreliable computation can lead to very serious consequences. Hence reliability questions stand are at the forefront of engineering and theoretical interests. This book presents the mathematical theory of the finite element method and is the first to focus on the questions of how reliable computed results really are. It addresses among other topics the local behaviour, errors caused by pollution, superconvergence, and optimal meshes. Many computational examples illustrate the importance of the theoretical conclusions for practical computations. Graduate students, lecturers, and researchers in mathematics, engineering, and scientific computation will benefit from the clear structure of the book, and will find this a very useful reference.

Mathematical Aspects of Finite Elements in Partial Differential Equations

Carl de Boor
Mathematical Aspects of Finite Elements in Partial Differential Equations Book PDF

Author : Carl de Boor
Publisher : Academic Press
Page : 430 pages
File Size : 44,7 Mb
Release : 2014-05-10
Category : Mathematics
ISBN : 9781483268071

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Mathematical Aspects of Finite Elements in Partial Differential Equations by Carl de Boor Pdf

Mathematical Aspects of Finite Elements in Partial Differential Equations addresses the mathematical questions raised by the use of finite elements in the numerical solution of partial differential equations. This book covers a variety of topics, including finite element method, hyperbolic partial differential equation, and problems with interfaces. Organized into 13 chapters, this book begins with an overview of the class of finite element subspaces with numerical examples. This text then presents as models the Dirichlet problem for the potential and bipotential operator and discusses the question of non-conforming elements using the classical Ritz- and least-squares-method. Other chapters consider some error estimates for the Galerkin problem by such energy considerations. This book discusses as well the spatial discretization of problem and presents the Galerkin method for ordinary differential equations using polynomials of degree k. The final chapter deals with the continuous-time Galerkin method for the heat equation. This book is a valuable resource for mathematicians.

Finite Element Methods

Jonathan Whiteley
Finite Element Methods Book PDF

Author : Jonathan Whiteley
Publisher : Springer
Page : 232 pages
File Size : 43,7 Mb
Release : 2017-01-26
Category : Science
ISBN : 9783319499710

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Finite Element Methods by Jonathan Whiteley Pdf

This book presents practical applications of the finite element method to general differential equations. The underlying strategy of deriving the finite element solution is introduced using linear ordinary differential equations, thus allowing the basic concepts of the finite element solution to be introduced without being obscured by the additional mathematical detail required when applying this technique to partial differential equations. The author generalizes the presented approach to partial differential equations which include nonlinearities. The book also includes variations of the finite element method such as different classes of meshes and basic functions. Practical application of the theory is emphasised, with development of all concepts leading ultimately to a description of their computational implementation illustrated using Matlab functions. The target audience primarily comprises applied researchers and practitioners in engineering, but the book may also be beneficial for graduate students.

The Mathematical Basis of Finite Element Methods

David Francis Griffiths
The Mathematical Basis of Finite Element Methods Book PDF

Author : David Francis Griffiths
Publisher : Unknown
Page : 189 pages
File Size : 53,5 Mb
Release : 1986
Category : Electronic
ISBN : OCLC:927523539

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The Mathematical Basis of Finite Element Methods by David Francis Griffiths Pdf