An Adaptive Finite Element Method For Pointwise Error Control
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An Adaptive Finite Element Method For Pointwise Error Control
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Author : Renu Dhadwal
language : en
Publisher:
Release Date : 2000
An Adaptive Finite Element Method For Pointwise Error Control written by Renu Dhadwal and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with categories.
Error Controlled Adaptive Finite Elements In Solid Mechanics
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Author : Ekkehard Ramm
language : en
Publisher: John Wiley & Sons
Release Date : 2003-08-01
Error Controlled Adaptive Finite Elements In Solid Mechanics written by Ekkehard Ramm 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 2003-08-01 with Technology & Engineering categories.
Finite Element Methods are used for numerous engineering applications where numerical solutions of partial differential equations are needed. As computers can now deal with the millions of parameters used in these methods, automatic error estimation and automatic adaptation of the utilised method (according to this error estimation), has become a hot research topic. This text offers comprehensive coverage of this new field of automatic adaptation and error estimation, bringing together the work of eight outstanding researchers in this field who have completed a six year national research project within the German Science Foundation. The result is a state-of-the-art work in true reference style. Each chapter is self-contained and covers theoretical, algorithmic and software presentations as well as solved problems. A main feature consists of several carefully elaborated benchmarks of 2D- and 3D- applications. * First book to go beyond the Finite Element Method in itself * Covers material from a new research area * Presents benchmarks of 2D- and 3D- applications * Fits with the new trend for genetic strategies in engineering
An A Posteriori Error Analysis For Distributed Elliptic Optimal Control Problems With Pointwise State Constraints
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Author :
language : en
Publisher:
Release Date : 2007
An A Posteriori Error Analysis For Distributed Elliptic Optimal Control Problems With Pointwise State Constraints written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with categories.
This thesis is concerned with the development, analysis, and implementation of an adaptive finite element method for distributed elliptic optimal control problems with pointwise unilateral constraints on the state. In particular, two residual-type a posteriori error estimators will be derived. The first one takes advantage of the modified adjoint state, which is defined as some kind of regularization of the adjoint state. Furthermore, this error estimator will, after minor modification, be transfered to the Lavrentiev regularization of the pure state constrained case. Up to a consistency error and data oscillation, reliability and efficiency results concerning the approximation of the state, the control, and the modified adjoint state can be provided for these error estimators. With two numerical examples, the performance of the adaptive algorithm will be investigated. A benefit compared to an uniform refinement strategy will be noticeable. The second developed a posteriori error estimator results from a measure extension of the discrete measure appearing in the right-hand side of the adjoint state equation to an element in the space of square integrable functions. This error estimator provides, again up to a consistency error and data oscillation, reliability and efficiency for the approximation error in the control, in the state, and in a semi-continuous auxiliary adjoint state. Another numerical example will show that this error estimator might be advantageous.
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
Adaptive Finite Element Methods
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Author : Wenbin Liu
language : en
Publisher: Alpha Science International Limited
Release Date : 2012
Adaptive Finite Element Methods written by Wenbin Liu and has been published by Alpha Science International Limited this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Mathematics categories.
Summary: "This book emphasizes the discussions of some unique issues from the adaptive finite element approximation of optimal control. The main idea used in the approximation error analysis (both a priori and a posteriori) is to first combine convex analysis and interpolation error estimations of suitable interpolators, which much depend on the structure of the control constraints, to derive the error estimates for the control via the variational inequalities in the optimality conditions, and then to apply the standard techniques to derive the error estimates for the state equations. The need, the framework and the techniques of using multi adaptive meshes in developing efficient numerical algorithms for optimal control have been emphasized throughout the book. The book starts from several typical examples of optimal control problems and then discusses existence and optimality conditions for some optimal control problems. It is believed that these discussions are especially useful for the researchers and students who first entered this area. Then the finite element approximation schemes for several typical optimal control problems are set up, their a priori and a posteriori error estimates are derived following the main idea mentioned, and their computational methods are studied."-- Publisher website, viewed 13th July, 2012.
An Adaptive Finite Element Method With Efficient Maximum Norm Error Control For Elliptic Problems
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Author : Kenneth Eriksson
language : en
Publisher:
Release Date : 1993
An Adaptive Finite Element Method With Efficient Maximum Norm Error Control For Elliptic Problems written by Kenneth Eriksson and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with categories.
Error Estimation And Adaptive Discretization Methods In Computational Fluid Dynamics
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Author : Timothy J. Barth
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Error Estimation And Adaptive Discretization Methods In Computational Fluid Dynamics written by Timothy J. Barth 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 2013-04-17 with Mathematics categories.
As computational fluid dynamics (CFD) is applied to ever more demanding fluid flow problems, the ability to compute numerical fluid flow solutions to a user specified tolerance as well as the ability to quantify the accuracy of an existing numerical solution are seen as essential ingredients in robust numerical simulation. Although the task of accurate error estimation for the nonlinear equations of CFD seems a daunting problem, considerable effort has centered on this challenge in recent years with notable progress being made by the use of advanced error estimation techniques and adaptive discretization methods. To address this important topic, a special course wasjointly organized by the NATO Research and Technology Office (RTO), the von Karman Insti tute for Fluid Dynamics, and the NASA Ames Research Center. The NATO RTO sponsored course entitled "Error Estimation and Solution Adaptive Discretization in CFD" was held September 10-14, 2002 at the NASA Ames Research Center and October 15-19, 2002 at the von Karman Institute in Belgium. During the special course, a series of comprehensive lectures by leading experts discussed recent advances and technical progress in the area of numerical error estimation and adaptive discretization methods with spe cific emphasis on computational fluid dynamics. The lecture notes provided in this volume are derived from the special course material. The volume con sists of 6 articles prepared by the special course lecturers.
Adaptive Error Control In The Finite Element Method For Time Dependent Problems
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Author : Peter K. Jimack
language : en
Publisher:
Release Date : 1992
Adaptive Error Control In The Finite Element Method For Time Dependent Problems written by Peter K. Jimack and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Finite element method categories.
The general approach is then applied to a class of convection- diffusion problems where a particular estimate of this new spatial error is discussed. This estimate is based upon obtaining an improved approximation to the time derivative, in this case by using a richer but less regular trial space, which is then compared with the approximation that is actually used. A number of numerical examples are included which demonstrate the success of the strategy in conjunction with an adaptive h- refinement and derefinement procedure. This adaptivity algorithm is described in some detail for the case of a mesh of triangles in 2-d."
Error Controlled Hp Adaptive Finite Element Methods For The Time Dependent Maxwell Equations
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Author : Martin Lilienthal
language : en
Publisher:
Release Date : 2015
Error Controlled Hp Adaptive Finite Element Methods For The Time Dependent Maxwell Equations written by Martin Lilienthal and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with categories.
A Unified Approach To The Finite Element Method And Error Analysis Procedures
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Author : Julian A. T. Dow
language : en
Publisher: Elsevier
Release Date : 1998-11-09
A Unified Approach To The Finite Element Method And Error Analysis Procedures written by Julian A. T. Dow and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-11-09 with Technology & Engineering categories.
A Unified Approach to the Finite Element Method and Error Analysis Procedures provides an in-depth background to better understanding of finite element results and techniques for improving accuracy of finite element methods. Thus, the reader is able to identify and eliminate errors contained in finite element models. Three different error analysis techniques are systematically developed from a common theoretical foundation: 1) modeling erros in individual elements; 2) discretization errors in the overall model; 3) point-wise errors in the final stress or strain results. Thoroughly class tested with undergraduate and graduate students. A Unified Approach to the Finite Element Method and Error Analysis Procedures is sure to become an essential resource for students as well as practicing engineers and researchers. New, simpler element formulation techniques, model-independent results, and error measures New polynomial-based methods for identifying critical points New procedures for evaluating sheer/strain accuracy Accessible to undergraduates, insightful to researchers, and useful to practitioners Taylor series (polynomial) based Intuitive elemental and point-wise error measures Essential background information provided in 12 appendices