Finite Element Analysis With Error Estimators
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Finite Element Analysis With Error Estimators
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Author : J. E. Akin
language : en
Publisher: Elsevier
Release Date : 2005-06-22
Finite Element Analysis With Error Estimators written by J. E. Akin and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-06-22 with Technology & Engineering categories.
This key text is written for senior undergraduate and graduate engineering students. It delivers a complete introduction to finite element methods and to automatic adaptation (error estimation) that will enable students to understand and use FEA as a true engineering tool. It has been specifically developed to be accessible to non-mathematics students and provides the only complete text for FEA with error estimators for non-mathematicians. Error estimation is taught on nearly half of all FEM courses for engineers at senior undergraduate and postgraduate level; no other existing textbook for this market covers this topic. The only introductory FEA text with error estimation for students of engineering, scientific computing and applied mathematics Includes source code for creating and proving FEA error estimators
A Posteriori Error Estimation In Finite Element Analysis
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Author : Mark Ainsworth
language : en
Publisher: John Wiley & Sons
Release Date : 2011-09-28
A Posteriori Error Estimation In Finite Element Analysis written by Mark Ainsworth and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-09-28 with Mathematics categories.
An up-to-date, one-stop reference-complete with applications This volume presents the most up-to-date information available on aposteriori error estimation for finite element approximation inmechanics and mathematics. It emphasizes methods for ellipticboundary value problems and includes applications to incompressibleflow and nonlinear problems. Recent years have seen an explosion in the study of a posteriorierror estimators due to their remarkable influence on improvingboth accuracy and reliability in scientific computing. In an effortto provide an accessible source, the authors have sought to presentkey ideas and common principles on a sound mathematicalfooting. Topics covered in this timely reference include: * Implicit and explicit a posteriori error estimators * Recovery-based error estimators * Estimators, indicators, and hierarchic bases * The equilibrated residual method * Methodology for the comparison of estimators * Estimation of errors in quantities of interest A Posteriori Error Estimation in Finite Element Analysis is a lucidand convenient resource for researchers in almost any field offinite element methods, and for applied mathematicians andengineers who have an interest in error estimation and/or finiteelements.
Finite Elements
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Author : Ivo Babuska
language : en
Publisher: Oxford University Press
Release Date : 2010-11-04
Finite Elements written by Ivo Babuska and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-11-04 with Mathematics categories.
Most of the many books on finite elements are devoted either to mathematical theory or to engineering applications, but not to both. This book presents computed numbers which not only illustrate the theory but can only be analysed using the theory. This approach, both dual and interacting between theory and computation makes this book unique.
A Posteriori Error Estimation In Finite Element Analysis
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Author : Mark Ainsworth
language : en
Publisher:
Release Date : 1996
A Posteriori Error Estimation In Finite Element Analysis written by Mark Ainsworth and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with categories.
A Posteriori Error Estimation Techniques For Finite Element Methods
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Author : Rudiger Verfurth
language : en
Publisher: Oxford University Press
Release Date : 2013-04-18
A Posteriori Error Estimation Techniques For Finite Element Methods written by Rudiger Verfurth and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-18 with Mathematics categories.
A posteriori error estimation techniques are fundamental to the efficient numerical solution of PDEs arising in physical and technical applications. This book gives a unified approach to these techniques and guides graduate students, researchers, and practitioners towards understanding, applying and developing self-adaptive discretization methods.
Finite Element Analysis
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Author : Barna Szabó
language : en
Publisher: John Wiley & Sons
Release Date : 1991-09-03
Finite Element Analysis written by Barna Szabó and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991-09-03 with Technology & Engineering categories.
Covers the fundamentals of linear theory of finite elements, from both mathematical and physical points of view. Major focus is on error estimation and adaptive methods used to increase the reliability of results. Incorporates recent advances not covered by other books.
Nonlinear Finite Element Analysis In Structural Mechanics
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Author : W. Wunderlich
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
Nonlinear Finite Element Analysis In Structural Mechanics written by W. Wunderlich and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Science categories.
With the rap1d development of computational capab1lities, nonl1near f1nite element analys1s 1n structural mechan1CS has become an 1mportant field of research. Its objective is the real1stic assessment of the actual behaV10r of structures by numerical methods. Th1S requires that all nonlinear effects, such as the nonl1near character1stics of the mater1al and large deformations be taken 1nto account. The act1vities in th1S f1eld be1ng worldw1de, d1rect 1nteraction between the various research groups 1S necessary to coordinate future research and to overcome the time gap between the generat10n of new results and the1r appearance 1n the 11terature. The f1rst U.S.-Germany Sympos1um was held 1n 1976 at the Massachusetts Inst1tute of Technology. Under the general to P1C "Formulat1ons and Computat1onal Algorithms in Fin1te Ele ment Analysis" 1t prov1ded an opportun1ty for about 20 re searchers from each country to present lectures, hold discus sions, and establ1sh mutual contacts. The success of th1S first sympos1um was so encourag1ng that 1t seemed natural to organ- 1ze a second bilateral meet1ng, this time 1n Germany, and to 1nv1te researchers from other European countr1es as well
The Finite Element Method And Its Reliability
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Author : Ivo Babuška
language : en
Publisher: Oxford University Press
Release Date : 2001
The Finite Element Method And Its Reliability written by Ivo Babuška and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Mathematics categories.
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.
Advances In A Posteriori Error Estimation On Anisotropic Finite Element Discretizations
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Author : Gerd Kunert
language : en
Publisher: Logos Verlag Berlin
Release Date : 2003
Advances In A Posteriori Error Estimation On Anisotropic Finite Element Discretizations written by Gerd Kunert and has been published by Logos Verlag Berlin this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Finite element method categories.
Certain classes of partial differential equations generically give rise to solutions with strong directional features, e.g. with boundary layers. Such solutions are called anisotropic. Their discretization by means of the finite element method (for example) can favourably employ so-called anisotropic meshes. These meshes are characterized by stretched, anisotropic finite elements with a (very) large stretching ratio. The widespread use of computer simulation leads to an increasing demand for semi- or fully automatic solution procedures. Within such self-adaptive algorithms, a posteriori error estimators form an indispensable ingredient for quality control. They are well understood for standard, isotropic discretizations. The knowledge about a posteriori error estimation on anisotropic meshes is much less mature. During the last decade the foundation and basic principles have been proposed, discussed and established, mostly for the Poisson problem. This monograph summarises some of the recent advances in anisotropic error estimation for more challenging problems. Emphasis is given to the contributions of the author. In Chapter 3 the investigation starts with singularly perturbed reaction diffusion problems which frequently lead to solutions with boundary layers. This problem class often arises when simplifying more complex models. Chapter 4 treats singularly perturbed convection diffusion problems, i.e. the convection is dominating. The solution structure is more intricate, and often features boundary layer and/or interior layer solutions. Chapter 5 is devoted to the Stokes equations. Flow problems generically give rise to anisotropic solutions (e.g. with edge singularities or containing layers). The Stokes equations often serve as a simplified or linearised model. In all three chapters, the main results consist in error estimators and corresponding error bounds that are robust with respect to the mesh anisotropy, as far as possible. Finally Chapter 6 addresses the robustness of a posteriori error estimation with respect to the mesh anisotropy.In particular the relation between anisotropic mesh construction and error estimation is investigated. This thesis presents the philosophy of anisotropic error estimation as well as the main results and the definitions required. Proofs and technical details are omitted; instead the key ideas are explained.The compact style of presentation aims at practitioners in particular by providing easily accessible error estimators and error bounds. Further insight is readily possible through the references.
The Mathematical Theory Of Finite Element Methods
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Author : Susanne Brenner
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-12-22
The Mathematical Theory Of Finite Element Methods written by Susanne Brenner and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-12-22 with Mathematics categories.
This is the third and yet further updated edition of a highly regarded mathematical text. Brenner develops the basic mathematical theory of the finite element method, the most widely used technique for engineering design and analysis. Her volume formalizes basic tools that are commonly used by researchers in the field but not previously published. The book is ideal for mathematicians as well as engineers and physical scientists. It can be used for a course that provides an introduction to basic functional analysis, approximation theory, and numerical analysis, while building upon and applying basic techniques of real variable theory. This new edition is substantially updated with additional exercises throughout and new chapters on Additive Schwarz Preconditioners and Adaptive Meshes.