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

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Publisher : Academic Press
ISBN 13 : 1483267989
Total Pages : 814 pages
Book Rating : 4.4/5 (832 download)

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

Download or read book The Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations written by A. K. Aziz and published by Academic Press. This book was released on 2014-05-10 with total page 814 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

The Mathematical Basis of Finite Element Methods

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Publisher :
ISBN 13 :
Total Pages : 189 pages
Book Rating : 4.:/5 (927 download)

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Book Synopsis The Mathematical Basis of Finite Element Methods by : David Francis Griffiths

Download or read book The Mathematical Basis of Finite Element Methods written by David Francis Griffiths and published by . This book was released on 1986 with total page 189 pages. Available in PDF, EPUB and Kindle. Book excerpt:

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

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Publisher : Oxford University Press, USA
ISBN 13 :
Total Pages : 208 pages
Book Rating : 4.:/5 (45 download)

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

Download or read book The Mathematical Basis of Finite Element Methods with Applications to Partial Differential Equations written by Institute of Mathematics and Its Applications and published by Oxford University Press, USA. This book was released on 1984 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 Mathematical Basis of Finite Element Methods with Applications to Partial Differential Equations

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Publisher :
ISBN 13 :
Total Pages : 189 pages
Book Rating : 4.:/5 (449 download)

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Book Synopsis The Mathematical Basis of Finite Element Methods with Applications to Partial Differential Equations by : David F. GRIFFITHS

Download or read book The Mathematical Basis of Finite Element Methods with Applications to Partial Differential Equations written by David F. GRIFFITHS and published by . This book was released on 1984 with total page 189 pages. Available in PDF, EPUB and Kindle. Book excerpt:

The Finite Element Method: Theory, Implementation, and Applications

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Publisher : Springer Science & Business Media
ISBN 13 : 3642332870
Total Pages : 403 pages
Book Rating : 4.6/5 (423 download)

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Book Synopsis The Finite Element Method: Theory, Implementation, and Applications by : Mats G. Larson

Download or read book The Finite Element Method: Theory, Implementation, and Applications written by Mats G. Larson and published by Springer Science & Business Media. This book was released on 2013-01-13 with total page 403 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.​

Numerical Solution of Partial Differential Equations by the Finite Element Method

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Publisher : Courier Corporation
ISBN 13 : 0486131599
Total Pages : 290 pages
Book Rating : 4.4/5 (861 download)

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Book Synopsis Numerical Solution of Partial Differential Equations by the Finite Element Method by : Claes Johnson

Download or read book Numerical Solution of Partial Differential Equations by the Finite Element Method written by Claes Johnson and published by Courier Corporation. This book was released on 2012-05-23 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Finite Element Methods

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Publisher : Springer
ISBN 13 : 3319499718
Total Pages : 236 pages
Book Rating : 4.3/5 (194 download)

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Book Synopsis Finite Element Methods by : Jonathan Whiteley

Download or read book Finite Element Methods written by Jonathan Whiteley and published by Springer. This book was released on 2017-01-26 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 Finite Element Method for Elliptic Problems

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Publisher : Elsevier
ISBN 13 : 0080875254
Total Pages : 551 pages
Book Rating : 4.0/5 (88 download)

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Book Synopsis The Finite Element Method for Elliptic Problems by : P.G. Ciarlet

Download or read book The Finite Element Method for Elliptic Problems written by P.G. Ciarlet and published by Elsevier. This book was released on 1978-01-01 with total page 551 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations

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Publisher :
ISBN 13 :
Total Pages : 797 pages
Book Rating : 4.:/5 (911 download)

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

Download or read book The Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations written by A. K. Aziz and published by . This book was released on 1972 with total page 797 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Mathematical Foundations of Finite Elements and Iterative Solvers

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Publisher : SIAM
ISBN 13 : 1611977096
Total Pages : 186 pages
Book Rating : 4.6/5 (119 download)

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Book Synopsis Mathematical Foundations of Finite Elements and Iterative Solvers by : SCI085000

Download or read book Mathematical Foundations of Finite Elements and Iterative Solvers written by SCI085000 and published by SIAM. This book was released on 2022-06-27 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: “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.

Partial Differential Equations and the Finite Element Method

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Publisher : John Wiley & Sons
ISBN 13 : 0471764094
Total Pages : 505 pages
Book Rating : 4.4/5 (717 download)

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Book Synopsis Partial Differential Equations and the Finite Element Method by : Pavel Ŝolín

Download or read book Partial Differential Equations and the Finite Element Method written by Pavel Ŝolín and published by John Wiley & Sons. This book was released on 2005-12-16 with total page 505 pages. Available in PDF, EPUB and Kindle. Book excerpt: A systematic introduction to partial differential equations and modern finite element methods for their efficient numerical solution Partial Differential Equations and the Finite Element Method provides a much-needed, clear, and systematic introduction to modern theory of partial differential equations (PDEs) and finite element methods (FEM). Both nodal and hierachic concepts of the FEM are examined. Reflecting the growing complexity and multiscale nature of current engineering and scientific problems, the author emphasizes higher-order finite element methods such as the spectral or hp-FEM. A solid introduction to the theory of PDEs and FEM contained in Chapters 1-4 serves as the core and foundation of the publication. Chapter 5 is devoted to modern higher-order methods for the numerical solution of ordinary differential equations (ODEs) that arise in the semidiscretization of time-dependent PDEs by the Method of Lines (MOL). Chapter 6 discusses fourth-order PDEs rooted in the bending of elastic beams and plates and approximates their solution by means of higher-order Hermite and Argyris elements. Finally, Chapter 7 introduces the reader to various PDEs governing computational electromagnetics and describes their finite element approximation, including modern higher-order edge elements for Maxwell's equations. The understanding of many theoretical and practical aspects of both PDEs and FEM requires a solid knowledge of linear algebra and elementary functional analysis, such as functions and linear operators in the Lebesgue, Hilbert, and Sobolev spaces. These topics are discussed with the help of many illustrative examples in Appendix A, which is provided as a service for those readers who need to gain the necessary background or require a refresher tutorial. Appendix B presents several finite element computations rooted in practical engineering problems and demonstrates the benefits of using higher-order FEM. Numerous finite element algorithms are written out in detail alongside implementation discussions. Exercises, including many that involve programming the FEM, are designed to assist the reader in solving typical problems in engineering and science. Specifically designed as a coursebook, this student-tested publication is geared to upper-level undergraduates and graduate students in all disciplines of computational engineeringand science. It is also a practical problem-solving reference for researchers, engineers, and physicists.

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

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Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (141 download)

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Book Synopsis The Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations by :

Download or read book The Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations written by and published by . This book was released on 1972 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Mathematical and Numerical Methods for Partial Differential Equations

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Publisher : Springer
ISBN 13 : 3319035630
Total Pages : 362 pages
Book Rating : 4.3/5 (19 download)

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Book Synopsis Mathematical and Numerical Methods for Partial Differential Equations by : Joël Chaskalovic

Download or read book Mathematical and Numerical Methods for Partial Differential Equations written by Joël Chaskalovic and published by Springer. This book was released on 2014-05-16 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: This self-tutorial offers a concise yet thorough introduction into the mathematical analysis of approximation methods for partial differential equation. A particular emphasis is put on finite element methods. The unique approach first summarizes and outlines the finite-element mathematics in general and then in the second and major part, formulates problem examples that clearly demonstrate the techniques of functional analysis via numerous and diverse exercises. The solutions of the problems are given directly afterwards. Using this approach, the author motivates and encourages the reader to actively acquire the knowledge of finite- element methods instead of passively absorbing the material as in most standard textbooks. This English edition is based on the Finite Element Methods for Engineering Sciences by Joel Chaskalovic.

˜Theœ mathematical foundations of the finite element method with applications to partial differential equations

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Publisher :
ISBN 13 :
Total Pages : 797 pages
Book Rating : 4.:/5 (16 download)

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Book Synopsis ˜Theœ mathematical foundations of the finite element method with applications to partial differential equations by : Abdul Kadir Aziz

Download or read book ˜Theœ mathematical foundations of the finite element method with applications to partial differential equations written by Abdul Kadir Aziz and published by . This book was released on 1972 with total page 797 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Finite Element Methods and Their Applications

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Publisher : Springer Science & Business Media
ISBN 13 : 3540240780
Total Pages : 415 pages
Book Rating : 4.5/5 (42 download)

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Book Synopsis Finite Element Methods and Their Applications by : Zhangxin Chen

Download or read book Finite Element Methods and Their Applications written by Zhangxin Chen and published by Springer Science & Business Media. This book was released on 2005-06-23 with total page 415 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduce every concept in the simplest setting and to maintain a level of treatment that is as rigorous as possible without being unnecessarily abstract. Contains unique recent developments of various finite elements such as nonconforming, mixed, discontinuous, characteristic, and adaptive finite elements, along with their applications. Describes unique recent applications of finite element methods to important fields such as multiphase flows in porous media and semiconductor modelling. Treats the three major types of partial differential equations, i.e., elliptic, parabolic, and hyperbolic equations.

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

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Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (472 download)

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

Download or read book The Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations written by A. K. Aziz and published by . This book was released on 1972 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

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

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Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (499 download)

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Book Synopsis The Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations by : Abdul K. Aziz

Download or read book The Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations written by Abdul K. Aziz and published by . This book was released on 1972 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: