Mathematical Aspects Of Finite Elements In Partial Differential Equations

Author : Carl de Boor
Publisher : Academic Press
ISBN 13 : 1483268071
Total Pages : 431 pages
Book Rating : 4.71/5 ( download)

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Download or read book Mathematical Aspects of Finite Elements in Partial Differential Equations written by Carl de Boor and published by Academic Press. This book was released on 2014-05-10 with total page 431 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : University of Wisconsin. MATHEMATICS RESEARCH CENTER.
Publisher :
ISBN 13 :
Total Pages : 420 pages
Book Rating : 4.35/5 ( download)

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Download or read book Mathematical Aspects of finite elements in partial differential equations written by University of Wisconsin. MATHEMATICS RESEARCH CENTER. and published by . This book was released on 1974 with total page 420 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : A. K. Aziz
Publisher : Academic Press
ISBN 13 : 1483267989
Total Pages : 814 pages
Book Rating : 4.82/5 ( download)

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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.

Author : Carl De Boor
Publisher :
ISBN 13 :
Total Pages : 420 pages
Book Rating : 4.12/5 ( download)

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Download or read book Mathematical aspects of finite elements in partial differential equations written by Carl De Boor and published by . This book was released on 1974 with total page 420 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : I. Galligani
Publisher : Springer
ISBN 13 : 3540371583
Total Pages : 371 pages
Book Rating : 4.88/5 ( download)

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Download or read book Mathematical Aspects of Finite Element Methods written by I. Galligani and published by Springer. This book was released on 2006-11-15 with total page 371 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Carl De Boor
Publisher :
ISBN 13 :
Total Pages : 420 pages
Book Rating : 4.12/5 ( download)

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Download or read book Mathematical Aspects of Finite Elements in Partial written by Carl De Boor and published by . This book was released on 1974 with total page 420 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Claes Johnson
Publisher : Courier Corporation
ISBN 13 : 0486131599
Total Pages : 290 pages
Book Rating : 4.97/5 ( download)

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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.

Author : Mats G. Larson
Publisher : Springer Science & Business Media
ISBN 13 : 3642332870
Total Pages : 403 pages
Book Rating : 4.76/5 ( download)

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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.​

Author :
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.35/5 ( download)

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Download or read book Mathematical Aspects of Finite Elements in Partial Differential Equations written by and published by . This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Pavel Ŝolín
Publisher : John Wiley & Sons
ISBN 13 : 0471764094
Total Pages : 505 pages
Book Rating : 4.90/5 ( download)

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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.