A Posteriori Error Estimation For Finite Element And Generalized Finite Element Method
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A Posteriori Error Estimation For Finite Element And Generalized Finite Element Method
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Author : Ivo Babuska
language : en
Publisher:
Release Date : 1998
A Posteriori Error Estimation For Finite Element And Generalized Finite Element Method written by Ivo Babuska and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with categories.
A Posteriori Error Estimation Techniques For Finite Element Methods
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Author : Rüdiger Verfürth
language : en
Publisher: OUP Oxford
Release Date : 2013-04-18
A Posteriori Error Estimation Techniques For Finite Element Methods written by Rüdiger Verfürth and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-18 with Mathematics categories.
Self-adaptive discretization methods are now an indispensable tool for the numerical solution of partial differential equations that arise from physical and technical applications. The aim is to obtain a numerical solution within a prescribed tolerance using a minimal amount of work. The main tools in achieving this goal are a posteriori error estimates which give global and local information on the error of the numerical solution and which can easily be computed from the given numerical solution and the data of the differential equation. This book reviews the most frequently used a posteriori error estimation techniques and applies them to a broad class of linear and nonlinear elliptic and parabolic equations. Although there are various approaches to adaptivity and a posteriori error estimation, they are all based on a few common principles. The main aim of the book is to elaborate these basic principles and to give guidelines for developing adaptive schemes for new problems. Chapters 1 and 2 are quite elementary and present various error indicators and their use for mesh adaptation in the framework of a simple model problem. The basic principles are introduced using a minimal amount of notations and techniques providing a complete overview for the non-specialist. Chapters 4-6 on the other hand are more advanced and present a posteriori error estimates within a general framework using the technical tools collected in Chapter 3. Most sections close with a bibliographical remark which indicates the historical development and hints at further results.
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.
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.
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
The Finite Element Method For Parabolic Equations Ii A Posteriori Error Estimation And Adaptive Approach
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Author : M. Bieterman
language : en
Publisher:
Release Date : 1982
The Finite Element Method For Parabolic Equations Ii A Posteriori Error Estimation And Adaptive Approach written by M. Bieterman and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1982 with categories.
We extend in this paper the analysis of a posteriori estimates of the space discretization error presented in a previous paper (3) for time-independent space meshes. In the context of the model problem studied there, results are given relating the effectivity of the error estimator to properties of the solution, space, meshes, and manner in which the meshes change. A procedure based upon this theory is presented for the adaptive construction of time-dependent meshes. The results of some computational experiments show that this procedure is practically very effective and suggest that it can be used to control the space discretization error in more general problems. (Author).
A Procedure For A Posteriori Error Estimation For H P Finite Element Methods
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Author :
language : en
Publisher:
Release Date : 1992
A Procedure For A Posteriori Error Estimation For H P Finite Element Methods written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with categories.
A new approach to a posteriori error estimation is outlined which is applicable to general h-p finite element approximations of general classes of boundary value problems. The approach makes use of duality arguments and is based on the element residual method (ERM). Important aspects of the method are that it provides a systematic approach toward deriving element boundary conditions for the ERM; it leads to an upper bound for the global error in an appropriate energy norm; and it is valid for non-uniform and irregular h-p meshes. In the present exposition, a brief outline of the theoretical foundations of the method is given together with the results of its application to several representative problems. These results show that the approach is applicable to general linearly elliptic systems, including unsymmetrical operators, and that the method is valid for broad classes of linear and non- linear problems.
The Finite Element Method For Parabolic Equations I A Posteriori Error Estimation
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Author : M. Bieterman
language : en
Publisher:
Release Date : 1982
The Finite Element Method For Parabolic Equations I A Posteriori Error Estimation written by M. Bieterman and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1982 with categories.
In this first of two papers, computable a posteriori estimates of the space discretization error in the finite element method of lines solution of parabolic equations are analyzed for time-independent space meshes. The effectivity of the error estimator is related to conditions on the solution regularity, mesh family type, and asymptotic range for the mesh size. For clarity the results are limited to a model problem in which piecewise linear elements in one space dimension are used. The results extend straightforwardly to systems of equations and higher order elements in one space dimension, while the higher dimensional case requires additional considerations. The theory presented here provides the basis for the analysis and adaptive construction of time-dependent space meshes, which is the subject of the second paper. Computational results show that the approach is practically very effective and suggest that it can be used for solving more general problems. (Author).
A Posteriori Error Estimation In The Finite Element Method
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Author : Mark Ainsworth
language : en
Publisher:
Release Date : 1989
A Posteriori Error Estimation In The Finite Element Method 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 1989 with categories.
A Feedback Finite Element Method With A Posteriori Error Estimation
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Author : I. Babuska
language : en
Publisher:
Release Date : 1984
A Feedback Finite Element Method With A Posteriori Error Estimation written by I. Babuska and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984 with Finite element method categories.
This paper is the first in a series of three which discusses some theoretical and practical aspect of a feedback finite element method for solving systems of linear second order elliptic partial differential equations (with particular interest in classical linear elasticity). This first part introduces some nonstandard finite element spaces, though based on the usual square bilinear elements, permit local mesh refinement. The algebraic structure of these spaces and their approximation properties are analysed. An equivalent estimator for the H1 finite element error is developed.