The Finite Element Method for Boundary Value Problems

The Finite Element Method for Boundary Value Problems
Title The Finite Element Method for Boundary Value Problems PDF eBook
Author Karan S. Surana
Publisher CRC Press
Pages 824
Release 2016-11-17
Genre Science
ISBN 1498780512

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Written by two well-respected experts in the field, The Finite Element Method for Boundary Value Problems: Mathematics and Computations bridges the gap between applied mathematics and application-oriented computational studies using FEM. Mathematically rigorous, the FEM is presented as a method of approximation for differential operators that are mathematically classified as self-adjoint, non-self-adjoint, and non-linear, thus addressing totality of all BVPs in various areas of engineering, applied mathematics, and physical sciences. These classes of operators are utilized in various methods of approximation: Galerkin method, Petrov-Galerkin Method, weighted residual method, Galerkin method with weak form, least squares method based on residual functional, etc. to establish unconditionally stable finite element computational processes using calculus of variations. Readers are able to grasp the mathematical foundation of finite element method as well as its versatility of applications. h-, p-, and k-versions of finite element method, hierarchical approximations, convergence, error estimation, error computation, and adaptivity are additional significant aspects of this book.

Numerical Approximation Methods for Elliptic Boundary Value Problems

Numerical Approximation Methods for Elliptic Boundary Value Problems
Title Numerical Approximation Methods for Elliptic Boundary Value Problems PDF eBook
Author Olaf Steinbach
Publisher Springer Science & Business Media
Pages 392
Release 2007-12-22
Genre Mathematics
ISBN 0387688056

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This book presents a unified theory of the Finite Element Method and the Boundary Element Method for a numerical solution of second order elliptic boundary value problems. This includes the solvability, stability, and error analysis as well as efficient methods to solve the resulting linear systems. Applications are the potential equation, the system of linear elastostatics and the Stokes system. While there are textbooks on the finite element method, this is one of the first books on Theory of Boundary Element Methods. It is suitable for self study and exercises are included.

Finite Elements and Approximation

Finite Elements and Approximation
Title Finite Elements and Approximation PDF eBook
Author O. C. Zienkiewicz
Publisher Courier Corporation
Pages 356
Release 2013-04-22
Genre Technology & Engineering
ISBN 048631801X

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A powerful tool for the approximate solution of differential equations, the finite element is extensively used in industry and research. This book offers students of engineering and physics a comprehensive view of the principles involved, with numerous illustrative examples and exercises. Starting with continuum boundary value problems and the need for numerical discretization, the text examines finite difference methods, weighted residual methods in the context of continuous trial functions, and piecewise defined trial functions and the finite element method. Additional topics include higher order finite element approximation, mapping and numerical integration, variational methods, and partial discretization and time-dependent problems. A survey of generalized finite elements and error estimates concludes the text.

Approximation of Elliptic Boundary-Value Problems

Approximation of Elliptic Boundary-Value Problems
Title Approximation of Elliptic Boundary-Value Problems PDF eBook
Author Jean-Pierre Aubin
Publisher Courier Corporation
Pages 386
Release 2007-01-01
Genre Mathematics
ISBN 0486457915

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A marriage of the finite-differences method with variational methods for solving boundary-value problems, the finite-element method is superior in many ways to finite-differences alone. This self-contained text for advanced undergraduates and graduate students is intended to imbed this combination of methods into the framework of functional analysis and to explain its applications to approximation of nonhomogeneous boundary-value problems for elliptic operators. The treatment begins with a summary of the main results established in the book. Chapter 1 introduces the variational method and the finite-difference method in the simple case of second-order differential equations. Chapters 2 and 3 concern abstract approximations of Hilbert spaces and linear operators, and Chapters 4 and 5 study finite-element approximations of Sobolev spaces. The remaining four chapters consider several methods for approximating nonhomogeneous boundary-value problems for elliptic operators.

Finite Element Approximation of Boundary Value Problems

Finite Element Approximation of Boundary Value Problems
Title Finite Element Approximation of Boundary Value Problems PDF eBook
Author Franz Chouly
Publisher Springer Nature
Pages 161
Release
Genre
ISBN 3031725301

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The Finite Element Method for Elliptic Problems

The Finite Element Method for Elliptic Problems
Title The Finite Element Method for Elliptic Problems PDF eBook
Author P.G. Ciarlet
Publisher Elsevier
Pages 551
Release 1978-01-01
Genre Mathematics
ISBN 0080875254

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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.

Numerical Solution of Partial Differential Equations by the Finite Element Method

Numerical Solution of Partial Differential Equations by the Finite Element Method
Title Numerical Solution of Partial Differential Equations by the Finite Element Method PDF eBook
Author Claes Johnson
Publisher Courier Corporation
Pages 290
Release 2012-05-23
Genre Mathematics
ISBN 0486131599

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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.