[PDF] Finite Element Methods For Integrodifferential Equations eBook

Author : Chuanmiao Chen
Publisher : World Scientific
Page : 294 pages
File Size : 28,24 MB
Release : 1998
Category : Mathematics
ISBN : 9789810232634

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Recently, there has appeared a new type of evaluating partial differential equations with Volterra integral operators in various practical areas. Such equations possess new physical and mathematical properties. This monograph systematically discusses application of the finite element methods to numerical solution of integrodifferential equations. It will be useful for numerical analysts, mathematicians, physicists and engineers. Advanced undergraduates and graduate students should also find it beneficial.

Author : Chuan Miao Chen
Publisher : World Scientific
Page : 291 pages
File Size : 47,89 MB
Release : 1998-02-28
Category : Mathematics
ISBN : 9814496952

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Recently, there has appeared a new type of evaluating partial differential equations with Volterra integral operators in various practical areas. Such equations possess new physical and mathematical properties. This monograph systematically discusses application of the finite element methods to numerical solution of integrodifferential equations. It will be useful for numerical analysts, mathematicians, physicists and engineers. Advanced undergraduates and graduate students should also find it beneficial.

Author : Mohammad Asadzadeh
Publisher : John Wiley & Sons
Page : 352 pages
File Size : 37,81 MB
Release : 2020-08-27
Category : Mathematics
ISBN : 1119671663

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Master the finite element method with this masterful and practical volume An Introduction to the Finite Element Method (FEM) for Differential Equations provides readers with a practical and approachable examination of the use of the finite element method in mathematics. Author Mohammad Asadzadeh covers basic FEM theory, both in one-dimensional and higher dimensional cases. The book is filled with concrete strategies and useful methods to simplify its complex mathematical contents. Practically written and carefully detailed, An Introduction to the Finite Element Method covers topics including: An introduction to basic ordinary and partial differential equations The concept of fundamental solutions using Green's function approaches Polynomial approximations and interpolations, quadrature rules, and iterative numerical methods to solve linear systems of equations Higher-dimensional interpolation procedures Stability and convergence analysis of FEM for differential equations This book is ideal for upper-level undergraduate and graduate students in natural science and engineering. It belongs on the shelf of anyone seeking to improve their understanding of differential equations.

Author : Zhangxin Chen
Publisher : Springer Science & Business Media
Page : 415 pages
File Size : 49,8 MB
Release : 2005-06-23
Category : Science
ISBN : 3540240780

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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.

Author : Jonathan Whiteley
Publisher : Springer
Page : 236 pages
File Size : 24,53 MB
Release : 2017-01-26
Category : Science
ISBN : 3319499718

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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.

Author : A. K. Aziz
Publisher : Academic Press
Page : 814 pages
File Size : 50,28 MB
Release : 2014-05-10
Category : Technology & Engineering
ISBN : 1483267989

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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 : Thomas Apel
Publisher : Springer
Page : 428 pages
File Size : 42,23 MB
Release : 2019-06-28
Category : Mathematics
ISBN : 3030142442

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Finite element methods are the most popular methods for solving partial differential equations numerically, and despite having a history of more than 50 years, there is still active research on their analysis, application and extension. This book features overview papers and original research articles from participants of the 30th Chemnitz Finite Element Symposium, which itself has a 40-year history. Covering topics including numerical methods for equations with fractional partial derivatives; isogeometric analysis and other novel discretization methods, like space-time finite elements and boundary elements; analysis of a posteriori error estimates and adaptive methods; enhancement of efficient solvers of the resulting systems of equations, discretization methods for partial differential equations on surfaces; and methods adapted to applications in solid and fluid mechanics, it offers readers insights into the latest results.

Author : Mats G. Larson
Publisher : Springer Science & Business Media
Page : 403 pages
File Size : 23,46 MB
Release : 2013-01-13
Category : Computers
ISBN : 3642332870

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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.​