Bounded And Positive Finite Element Approximations Of Reaction Diffusion Equations

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Bounded and Positive Finite Element Approximations of Reaction-Diffusion Equations

Author : Mohammed Althubyani
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (125 download)

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Book Synopsis Bounded and Positive Finite Element Approximations of Reaction-Diffusion Equations by : Mohammed Althubyani

Download or read book Bounded and Positive Finite Element Approximations of Reaction-Diffusion Equations written by Mohammed Althubyani and published by . This book was released on 2013 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Traditionally, the numerical analysis of di erential equations focusses on stability, convergence and accuracy of the numerical methods employed. However in practice, there are other features of the numerical methods that we are interested in. Generally, when we discretize a di erential equation, we would like to preserve certain intrinsic characteristics of the model, for example, positivity and boundedness of the quantities of interest. Consider- able progress has been made in this area for the Finite Di erence Method (FDM), for example, the Non Standard Finite Di erence Method (NSFDM). However, little work has been done on preserving positivity and bounded- ness for the numerical solutions of the Finite Element Method (FEM). In this work we develop a general framework for achieving this aim, which is based on the careful application of the Standard Galerkin FEM with 'Mass Lump- ing'. For concreteness, we present results for the Heat Equation, The Fisher reaction-di usion equation, and a coupled predator-prey reaction-di usion of Rosenzweig-MacArthur form.

On Reaction-diffusion Equations and Their Approximation by Finite Element Methods

Author : Stig Larsson
Publisher :
ISBN 13 : 9789170321887
Total Pages : 262 pages
Book Rating : 4.3/5 (218 download)

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Book Synopsis On Reaction-diffusion Equations and Their Approximation by Finite Element Methods by : Stig Larsson

Download or read book On Reaction-diffusion Equations and Their Approximation by Finite Element Methods written by Stig Larsson and published by . This book was released on 1985 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt:

On Reaction-diffusion Equation and Their Approximation by Finite Element Methods

Author : Stig Larsson
Publisher :
ISBN 13 :
Total Pages : 262 pages
Book Rating : 4.:/5 (785 download)

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Book Synopsis On Reaction-diffusion Equation and Their Approximation by Finite Element Methods by : Stig Larsson

Download or read book On Reaction-diffusion Equation and Their Approximation by Finite Element Methods written by Stig Larsson and published by . This book was released on 1985 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Reaction Diffusion Systems

Author : Gabriela Caristi
Publisher : CRC Press
ISBN 13 : 1000117197
Total Pages : 428 pages
Book Rating : 4.0/5 (1 download)

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Book Synopsis Reaction Diffusion Systems by : Gabriela Caristi

Download or read book Reaction Diffusion Systems written by Gabriela Caristi and published by CRC Press. This book was released on 2020-10-07 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Based on the proceedings of the International Conference on Reaction Diffusion Systems held recently at the University of Trieste, Italy. Presents new research papers and state-of-the-art surveys on the theory of elliptic, parabolic, and hyperbolic problems, and their related applications. Furnishes incisive contribution by over 40 mathematicians representing renowned institutions in North and South America, Europe, and the Middle East."

A Shadowing Result with Applications to Finite Element Approximation of Reaction-diffusion Equations

Author : Stig Larsson
Publisher :
ISBN 13 :
Total Pages : 17 pages
Book Rating : 4.:/5 (246 download)

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Book Synopsis A Shadowing Result with Applications to Finite Element Approximation of Reaction-diffusion Equations by : Stig Larsson

Download or read book A Shadowing Result with Applications to Finite Element Approximation of Reaction-diffusion Equations written by Stig Larsson and published by . This book was released on 1996 with total page 17 pages. Available in PDF, EPUB and Kindle. Book excerpt:

An Introduction to the Finite Element Method for Differential Equations

Author : Mohammad Asadzadeh
Publisher : John Wiley & Sons
ISBN 13 : 1119671663
Total Pages : 352 pages
Book Rating : 4.1/5 (196 download)

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Book Synopsis An Introduction to the Finite Element Method for Differential Equations by : Mohammad Asadzadeh

Download or read book An Introduction to the Finite Element Method for Differential Equations written by Mohammad Asadzadeh and published by John Wiley & Sons. This book was released on 2020-08-27 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Reaction-diffusion Equations And Their Applications And Computational Aspects - Proceedings Of The China-japan Symposium

Author : Tatsien Li
Publisher : World Scientific
ISBN 13 : 9814547840
Total Pages : 242 pages
Book Rating : 4.8/5 (145 download)

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Book Synopsis Reaction-diffusion Equations And Their Applications And Computational Aspects - Proceedings Of The China-japan Symposium by : Tatsien Li

Download or read book Reaction-diffusion Equations And Their Applications And Computational Aspects - Proceedings Of The China-japan Symposium written by Tatsien Li and published by World Scientific. This book was released on 1997-02-03 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of the symposium was to provide a forum for presenting and discussing recent developments and trends in Reaction-diffusion Equations and to promote scientific exchanges among mathematicians in China and in Japan, especially for the younger generation. The topics discussed were: Layer dynamics, Traveling wave solutions and its stability, Equilibrium solutions and its limit behavior (stability), Bifurcation phenomena, Computational solutions, and Infinite dimensional dynamical system.

The Finite Element Method

Author : A. J. Davies
Publisher : Oxford University Press
ISBN 13 : 0199609136
Total Pages : 308 pages
Book Rating : 4.1/5 (996 download)

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Book Synopsis The Finite Element Method by : A. J. Davies

Download or read book The Finite Element Method written by A. J. Davies and published by Oxford University Press. This book was released on 2011-09-08 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to the application of the finite element method to the solution of boundary and initial-value problems posed in terms of partial differential equations. Contains worked examples throughout and each chapter has a set of exercises with detailed solutions.

Estimating the Error of Numerical Solutions of Systems of Reaction-Diffusion Equations

Author : Donald J. Estep
Publisher : American Mathematical Soc.
ISBN 13 : 0821820729
Total Pages : 125 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Estimating the Error of Numerical Solutions of Systems of Reaction-Diffusion Equations by : Donald J. Estep

Download or read book Estimating the Error of Numerical Solutions of Systems of Reaction-Diffusion Equations written by Donald J. Estep and published by American Mathematical Soc.. This book was released on 2000 with total page 125 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper is concerned with the computational estimation of the error of numerical solutions of potentially degenerate reaction-diffusion equations. The underlying motivation is a desire to compute accurate estimates as opposed to deriving inaccurate analytic upper bounds. In this paper, we outline, analyze, and test an approach to obtain computational error estimates based on the introduction of the residual error of the numerical solution and in which the effects of the accumulation of errors are estimated computationally. We begin by deriving an a posteriori relationship between the error of a numerical solution and its residual error using a variational argument. This leads to the introduction of stability factors, which measure the sensitivity of solutions to various kinds of perturbations. Next, we perform some general analysis on the residual errors and stability factors to determine when they are defined and to bound their size. Then we describe the practical use of the theory to estimate the errors of numerical solutions computationally. Several key issues arise in the implementation that remain unresolved and we present partial results and numerical experiments about these points. We use this approach to estimate the error of numerical solutions of nine standard reaction-diffusion models and make a systematic comparison of the time scale over which accurate numerical solutions can be computed for these problems. We also perform a numerical test of the accuracy and reliability of the computational error estimate using the bistable equation. Finally, we apply the general theory to the class of problems that admit invariant regions for the solutions, which includes seven of the main examples. Under this additional stability assumption, we obtain a convergence result in the form of an upper bound on the error from the a posteriori error estimate. We conclude by discussing the preservation of invariant regions under discretization.

Galerkin Finite Element Methods for Parabolic Problems

Author : V. Thomee
Publisher : Springer
ISBN 13 : 3540387935
Total Pages : 243 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Galerkin Finite Element Methods for Parabolic Problems by : V. Thomee

Download or read book Galerkin Finite Element Methods for Parabolic Problems written by V. Thomee and published by Springer. This book was released on 2006-11-14 with total page 243 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Least-Squares Finite Element Methods

Author : Pavel B. Bochev
Publisher : Springer Science & Business Media
ISBN 13 : 0387689222
Total Pages : 669 pages
Book Rating : 4.3/5 (876 download)

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Book Synopsis Least-Squares Finite Element Methods by : Pavel B. Bochev

Download or read book Least-Squares Finite Element Methods written by Pavel B. Bochev and published by Springer Science & Business Media. This book was released on 2009-04-28 with total page 669 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since their emergence, finite element methods have taken a place as one of the most versatile and powerful methodologies for the approximate numerical solution of Partial Differential Equations. These methods are used in incompressible fluid flow, heat, transfer, and other problems. This book provides researchers and practitioners with a concise guide to the theory and practice of least-square finite element methods, their strengths and weaknesses, established successes, and open problems.

Numerical Solutions of Reaction-diffusion Equations

Author : Jianlin Cheng
Publisher :
ISBN 13 :
Total Pages : 112 pages
Book Rating : 4.:/5 (276 download)

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Book Synopsis Numerical Solutions of Reaction-diffusion Equations by : Jianlin Cheng

Download or read book Numerical Solutions of Reaction-diffusion Equations written by Jianlin Cheng and published by . This book was released on 1992 with total page 112 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Adaptive Finite Element Methods for Differential Equations

Author : Wolfgang Bangerth
Publisher : Springer Science & Business Media
ISBN 13 : 9783764370091
Total Pages : 222 pages
Book Rating : 4.3/5 (7 download)

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Book Synopsis Adaptive Finite Element Methods for Differential Equations by : Wolfgang Bangerth

Download or read book Adaptive Finite Element Methods for Differential Equations written by Wolfgang Bangerth and published by Springer Science & Business Media. This book was released on 2003-01-23 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt: The key issues are a posteriori error estimation and it automatic mesh adaptation. Besides the traditional approach of energy-norm error control, a new duality-based technique, the Dual Weighted Residual method for goal-oriented error estimation, is discussed in detail. This method aims at economical computation of arbitrary quantities of physical interest by properly adapting the computational mesh. This is typically required in the design cycles of technical applications. For example, the drag coefficient of a body immersed in a viscous flow is computed, then it is minimized by varying certain control parameters, and finally the stability of the resulting flow is investigated by solving an eigenvalue problem. `Goal-oriented' adaptivity is designed to achieve these tasks with minimal cost. At the end of each chapter some exercises are posed in order to assist the interested reader in better understanding the concepts presented. Solutions and accompanying remarks are given in the Appendix.

A Gauss-Galerkin Finite Element Method for a Class of Singular Diffusion Equations in Two Space Variables

Author : Li Liu
Publisher :
ISBN 13 :
Total Pages : 336 pages
Book Rating : 4.3/5 (129 download)

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Book Synopsis A Gauss-Galerkin Finite Element Method for a Class of Singular Diffusion Equations in Two Space Variables by : Li Liu

Download or read book A Gauss-Galerkin Finite Element Method for a Class of Singular Diffusion Equations in Two Space Variables written by Li Liu and published by . This book was released on 1998 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Stochastic Models for Fractional Calculus

Author : Mark M. Meerschaert
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110560240
Total Pages : 337 pages
Book Rating : 4.1/5 (15 download)

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Book Synopsis Stochastic Models for Fractional Calculus by : Mark M. Meerschaert

Download or read book Stochastic Models for Fractional Calculus written by Mark M. Meerschaert and published by Walter de Gruyter GmbH & Co KG. This book was released on 2019-10-21 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fractional calculus is a rapidly growing field of research, at the interface between probability, differential equations, and mathematical physics. It is used to model anomalous diffusion, in which a cloud of particles spreads in a different manner than traditional diffusion. This monograph develops the basic theory of fractional calculus and anomalous diffusion, from the point of view of probability. In this book, we will see how fractional calculus and anomalous diffusion can be understood at a deep and intuitive level, using ideas from probability. It covers basic limit theorems for random variables and random vectors with heavy tails. This includes regular variation, triangular arrays, infinitely divisible laws, random walks, and stochastic process convergence in the Skorokhod topology. The basic ideas of fractional calculus and anomalous diffusion are closely connected with heavy tail limit theorems. Heavy tails are applied in finance, insurance, physics, geophysics, cell biology, ecology, medicine, and computer engineering. The goal of this book is to prepare graduate students in probability for research in the area of fractional calculus, anomalous diffusion, and heavy tails. Many interesting problems in this area remain open. This book will guide the motivated reader to understand the essential background needed to read and unerstand current research papers, and to gain the insights and techniques needed to begin making their own contributions to this rapidly growing field.

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

Author : Abdul Kadir Aziz
Publisher :
ISBN 13 :
Total Pages : 822 pages
Book Rating : 4.3/5 (91 download)

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

Download or read book The 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 822 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations.

Introduction to Approximate Solution Techniques, Numerical Modeling, and Finite Element Methods

Author : Victor N. Kaliakin
Publisher : CRC Press
ISBN 13 : 9780824706791
Total Pages : 698 pages
Book Rating : 4.7/5 (67 download)

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Book Synopsis Introduction to Approximate Solution Techniques, Numerical Modeling, and Finite Element Methods by : Victor N. Kaliakin

Download or read book Introduction to Approximate Solution Techniques, Numerical Modeling, and Finite Element Methods written by Victor N. Kaliakin and published by CRC Press. This book was released on 2001-09-25 with total page 698 pages. Available in PDF, EPUB and Kindle. Book excerpt: Functions as a self-study guide for engineers and as a textbook for nonengineering students and engineering students, emphasizing generic forms of differential equations, applying approximate solution techniques to examples, and progressing to specific physical problems in modular, self-contained chapters that integrate into the text or can stand alone! This reference/text focuses on classical approximate solution techniques such as the finite difference method, the method of weighted residuals, and variation methods, culminating in an introduction to the finite element method (FEM). Discusses the general notion of approximate solutions and associated errors! With 1500 equations and more than 750 references, drawings, and tables, Introduction to Approximate Solution Techniques, Numerical Modeling, and Finite Element Methods: Describes the approximate solution of ordinary and partial differential equations using the finite difference method Covers the method of weighted residuals, including specific weighting and trial functions Considers variational methods Highlights all aspects associated with the formulation of finite element equations Outlines meshing of the solution domain, nodal specifications, solution of global equations, solution refinement, and assessment of results Containing appendices that present concise overviews of topics and serve as rudimentary tutorials for professionals and students without a background in computational mechanics, Introduction to Approximate Solution Techniques, Numerical Modeling, and Finite Element Methods is a blue-chip reference for civil, mechanical, structural, aerospace, and industrial engineers, and a practical text for upper-level undergraduate and graduate students studying approximate solution techniques and the FEM.