Superconvergence Of Finite Element Approximations For Pdes

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Superconvergence Of Finite Element Approximations For PDEs

Author : Rabee Jari
Publisher : LAP Lambert Academic Publishing
ISBN 13 : 9783659333170
Total Pages : 104 pages
Book Rating : 4.3/5 (331 download)

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Book Synopsis Superconvergence Of Finite Element Approximations For PDEs by : Rabee Jari

Download or read book Superconvergence Of Finite Element Approximations For PDEs written by Rabee Jari and published by LAP Lambert Academic Publishing. This book was released on 2013-01 with total page 104 pages. Available in PDF, EPUB and Kindle. Book excerpt: The finite element method (FEM) is a discretization technique for solving partial differential equations. It widely used in many fields of engineering such as computational fluid dynamics. The superconvergence of finite element solutions is an interesting and useful phenomenon in the scientific computing of real world problems and has become an area of active research in recent years. A general superconvergence of discontinuous Galerkin finite element method for the elliptic problem is established by using L DEGREES2-projection method. Regularity assumptions for the elliptic problem with regular partitions are required. Numerical experiments are given to verify the theoretical resu

Superconvergence of Finite Element Approximations for Partial Differential Equations

Author : Rabeea Hadi Jari
Publisher :
ISBN 13 :
Total Pages : 162 pages
Book Rating : 4.:/5 (819 download)

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Book Synopsis Superconvergence of Finite Element Approximations for Partial Differential Equations by : Rabeea Hadi Jari

Download or read book Superconvergence of Finite Element Approximations for Partial Differential Equations written by Rabeea Hadi Jari and published by . This book was released on 2012 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Finite Element Methods

Author : Michel Krizek
Publisher : Routledge
ISBN 13 : 1351448617
Total Pages : 368 pages
Book Rating : 4.3/5 (514 download)

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Book Synopsis Finite Element Methods by : Michel Krizek

Download or read book Finite Element Methods written by Michel Krizek and published by Routledge. This book was released on 2017-11-22 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: ""Based on the proceedings of the first conference on superconvergence held recently at the University of Jyvaskyla, Finland. Presents reviewed papers focusing on superconvergence phenomena in the finite element method. Surveys for the first time all known superconvergence techniques, including their proofs.

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

Author : A. K. Aziz
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.

Superconvergence in Galerkin Finite Element Methods

Author : Lars Wahlbin
Publisher : Springer
ISBN 13 : 3540494014
Total Pages : 179 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Superconvergence in Galerkin Finite Element Methods by : Lars Wahlbin

Download or read book Superconvergence in Galerkin Finite Element Methods written by Lars Wahlbin and published by Springer. This book was released on 2006-11-14 with total page 179 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is essentially a set of lecture notes from a graduate seminar given at Cornell in Spring 1994. It treats basic mathematical theory for superconvergence in the context of second order elliptic problems. It is aimed at graduate students and researchers. The necessary technical tools are developed in the text although sometimes long proofs are merely referenced. The book gives a rather complete overview of the field of superconvergence (in time-independent problems). It is the first text with such a scope. It includes a very complete and up-to-date list of references.

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 : 4.4/5 (832 download)

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Book Synopsis Mathematical Aspects of Finite Elements in Partial Differential Equations by : Carl de Boor

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.

Accuracy of Finite Element Approximations to Structural Problems

Author : Langley Research Center
Publisher :
ISBN 13 :
Total Pages : 60 pages
Book Rating : 4.:/5 (31 download)

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Book Synopsis Accuracy of Finite Element Approximations to Structural Problems by : Langley Research Center

Download or read book Accuracy of Finite Element Approximations to Structural Problems written by Langley Research Center and published by . This book was released on 1970 with total page 60 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Multilevel Finite Element Approximation

Author :
Publisher : Springer-Verlag
ISBN 13 : 3322912159
Total Pages : 160 pages
Book Rating : 4.3/5 (229 download)

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Book Synopsis Multilevel Finite Element Approximation by :

Download or read book Multilevel Finite Element Approximation written by and published by Springer-Verlag. This book was released on 2013-04-17 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt:

The Finite Element Method and Its Reliability

Author : Ivo Babuška
Publisher : Oxford University Press
ISBN 13 : 9780198502760
Total Pages : 820 pages
Book Rating : 4.5/5 (27 download)

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Book Synopsis The Finite Element Method and Its Reliability by : Ivo Babuška

Download or read book The Finite Element Method and Its Reliability written by Ivo Babuška and published by Oxford University Press. This book was released on 2001 with total page 820 pages. Available in PDF, EPUB and Kindle. Book excerpt: The finite element method is a numerical method widely used in engineering. Experience shows that unreliable computation can lead to very serious consequences. Hence reliability questions stand are at the forefront of engineering and theoretical interests. This book presents the mathematical theory of the finite element method and is the first to focus on the questions of how reliable computed results really are. It addresses among other topics the local behaviour, errors caused by pollution, superconvergence, and optimal meshes. Many computational examples illustrate the importance of the theoretical conclusions for practical computations. Graduate students, lecturers, and researchers in mathematics, engineering, and scientific computation will benefit from the clear structure of the book, and will find this a very useful reference.

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

Author : Institute of Mathematics and Its Applications
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.

Accuracy and Convergence of Finite Element Approximations

Author :
Publisher :
ISBN 13 :
Total Pages : 34 pages
Book Rating : 4.:/5 (227 download)

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Book Synopsis Accuracy and Convergence of Finite Element Approximations by :

Download or read book Accuracy and Convergence of Finite Element Approximations written by and published by . This book was released on 1968 with total page 34 pages. Available in PDF, EPUB and Kindle. Book excerpt: The paper reports on a theoretical investigation of the convergence properties of several finite element approximations in current use and assesses the magnitude of the principal errors resulting from their use for certain classes of structural problems. The method is based on classical order of error analyses commonly used to evaluate finite difference methods. Through the use of the Taylor series differential or partial differential equations are found which represent the convergence and principal error characteristics of the finite element equations. These resulting equations are then compared with known equations governing the continuum, and the error terms are evaluated for selected problems. Finite elements for bar, beam, plane stress, and plate bending problems are studied as well as the use of Straight or curved elements to approximate curved beams. The results of the study provide basic information on the effect of interelement compatibility, unequal size elements, discrepancies in triangular element approximations, flat element approximations to curved structures, and the number of elements required for a desired degree of accuracy.

Analysis of a Finite Element Method

Author : Granville Sewell
Publisher : Springer Science & Business Media
ISBN 13 : 1468463314
Total Pages : 163 pages
Book Rating : 4.4/5 (684 download)

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Book Synopsis Analysis of a Finite Element Method by : Granville Sewell

Download or read book Analysis of a Finite Element Method written by Granville Sewell and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 163 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text can be used for two quite different purposes. It can be used as a reference book for the PDElPROTRAN user· who wishes to know more about the methods employed by PDE/PROTRAN Edition 1 (or its predecessor, TWODEPEP) in solving two-dimensional partial differential equations. However, because PDE/PROTRAN solves such a wide class of problems, an outline of the algorithms contained in PDElPROTRAN is also quite suitable as a text for an introductory graduate level finite element course. Algorithms which solve elliptic, parabolic, hyperbolic, and eigenvalue partial differential equation problems are pre sented, as are techniques appropriate for treatment of singularities, curved boundaries, nonsymmetric and nonlinear problems, and systems of PDEs. Direct and iterative linear equation solvers are studied. Although the text emphasizes those algorithms which are actually implemented in PDEI PROTRAN, and does not discuss in detail one- and three-dimensional problems, or collocation and least squares finite element methods, for example, many of the most commonly used techniques are studied in detail. Algorithms applicable to general problems are naturally emphasized, and not special purpose algorithms which may be more efficient for specialized problems, such as Laplace's equation. It can be argued, however, that the student will better understand the finite element method after seeing the details of one successful implementation than after seeing a broad overview of the many types of elements, linear equation solvers, and other options in existence.

Convergence Rates for Finite Element Approximations of Stochastic Partial Differential Equations

Author : F. E. Benth
Publisher :
ISBN 13 : 9788255310303
Total Pages : 14 pages
Book Rating : 4.3/5 (13 download)

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Book Synopsis Convergence Rates for Finite Element Approximations of Stochastic Partial Differential Equations by : F. E. Benth

Download or read book Convergence Rates for Finite Element Approximations of Stochastic Partial Differential Equations written by F. E. Benth and published by . This book was released on 1996 with total page 14 pages. Available in PDF, EPUB and Kindle. Book excerpt:

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

Author : Victor N. Kaliakin
Publisher : CRC Press
ISBN 13 : 135199090X
Total Pages : 698 pages
Book Rating : 4.3/5 (519 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 2018-04-19 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.

Fitted Numerical Methods For Singular Perturbation Problems: Error Estimates In The Maximum Norm For Linear Problems In One And Two Dimensions (Revised Edition)

Download Fitted Numerical Methods For Singular Perturbation Problems: Error Estimates In The Maximum Norm For Linear Problems In One And Two Dimensions (Revised Edition) PDF Online Free

Author : John J H Miller
Publisher : World Scientific
ISBN 13 : 9814452777
Total Pages : 191 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Fitted Numerical Methods For Singular Perturbation Problems: Error Estimates In The Maximum Norm For Linear Problems In One And Two Dimensions (Revised Edition) by : John J H Miller

Download or read book Fitted Numerical Methods For Singular Perturbation Problems: Error Estimates In The Maximum Norm For Linear Problems In One And Two Dimensions (Revised Edition) written by John J H Miller and published by World Scientific. This book was released on 2012-02-29 with total page 191 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the first edition of this book, the literature on fitted mesh methods for singularly perturbed problems has expanded significantly. Over the intervening years, fitted meshes have been shown to be effective for an extensive set of singularly perturbed partial differential equations. In the revised version of this book, the reader will find an introduction to the basic theory associated with fitted numerical methods for singularly perturbed differential equations. Fitted mesh methods focus on the appropriate distribution of the mesh points for singularly perturbed problems. The global errors in the numerical approximations are measured in the pointwise maximum norm. The fitted mesh algorithm is particularly simple to implement in practice, but the theory of why these numerical methods work is far from simple. This book can be used as an introductory text to the theory underpinning fitted mesh methods.

Finite Element Approximations of High Order Partial Differential Equations

Author : Bin Zheng
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (435 download)

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Book Synopsis Finite Element Approximations of High Order Partial Differential Equations by : Bin Zheng

Download or read book Finite Element Approximations of High Order Partial Differential Equations written by Bin Zheng and published by . This book was released on 2008 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

N%-Superconvergence of Finite Element Approximations in the Interior of General Meshes of Triangles

Author :
Publisher :
ISBN 13 :
Total Pages : 192 pages
Book Rating : 4.:/5 (227 download)

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Book Synopsis N%-Superconvergence of Finite Element Approximations in the Interior of General Meshes of Triangles by :

Download or read book N%-Superconvergence of Finite Element Approximations in the Interior of General Meshes of Triangles written by and published by . This book was released on 1993 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper we introduce a new definition of super convergence - the n%-superconvergence, which generalizes the classical idea of superconvergence to general meshes. We show that this new definition can be employed to determine the regions of least error in any element in the interior of any grid by using a computer-based approach. We present numerical results for the standard displacement finite element method for the scalar equation of orthotropic heat- conduction. The results demonstrate that n% superconvergence is applicable to the complex grids which are employed in practical engineering computations.