A Posteriori Error Estimation For Nonlinear Problems By Duality Techniques
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A Posteriori Error Estimation For Nonlinear Problems By Duality Techniques
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Author : Eberhard Bänsch
language : en
Publisher:
Release Date : 1995
A Posteriori Error Estimation For Nonlinear Problems By Duality Techniques written by Eberhard Bänsch and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with categories.
A Posteriori Error Analysis Via Duality Theory
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Author : Weimin Han
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-07-30
A Posteriori Error Analysis Via Duality Theory written by Weimin Han 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 2006-07-30 with Mathematics categories.
This work provides a posteriori error analysis for mathematical idealizations in modeling boundary value problems, especially those arising in mechanical applications, and for numerical approximations of numerous nonlinear var- tional problems. An error estimate is called a posteriori if the computed solution is used in assessing its accuracy. A posteriori error estimation is central to m- suring, controlling and minimizing errors in modeling and numerical appr- imations. In this book, the main mathematical tool for the developments of a posteriori error estimates is the duality theory of convex analysis, documented in the well-known book by Ekeland and Temam ([49]). The duality theory has been found useful in mathematical programming, mechanics, numerical analysis, etc. The book is divided into six chapters. The first chapter reviews some basic notions and results from functional analysis, boundary value problems, elliptic variational inequalities, and finite element approximations. The most relevant part of the duality theory and convex analysis is briefly reviewed in Chapter 2.
A Posteriori Error Analysis Via Duality Theory
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Author : Weimin Han
language : en
Publisher: Springer
Release Date : 2004-11-19
A Posteriori Error Analysis Via Duality Theory written by Weimin Han and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-11-19 with Mathematics categories.
This work provides a posteriori error analysis for mathematical idealizations in modeling boundary value problems, especially those arising in mechanical applications, and for numerical approximations of numerous nonlinear var- tional problems. An error estimate is called a posteriori if the computed solution is used in assessing its accuracy. A posteriori error estimation is central to m- suring, controlling and minimizing errors in modeling and numerical appr- imations. In this book, the main mathematical tool for the developments of a posteriori error estimates is the duality theory of convex analysis, documented in the well-known book by Ekeland and Temam ([49]). The duality theory has been found useful in mathematical programming, mechanics, numerical analysis, etc. The book is divided into six chapters. The first chapter reviews some basic notions and results from functional analysis, boundary value problems, elliptic variational inequalities, and finite element approximations. The most relevant part of the duality theory and convex analysis is briefly reviewed in Chapter 2.
A Review Of Posteriori Error Estimation Adaptive Mesh Refinement Techniques
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Author : Rudiger Verfurth
language : en
Publisher: Wiley
Release Date : 1996-06-11
A Review Of Posteriori Error Estimation Adaptive Mesh Refinement Techniques written by Rudiger Verfurth and has been published by Wiley this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-06-11 with Mathematics categories.
Wiley—Teubner Series Advances in Numerical Mathematics Editors Hans Georg Bock Mitchell Luskin Wolfgang Hackbusch Rolf Rannacher A Review of A Posteriori Error Estimation and Adaptive Mesh-Refinement Techniques Rüdiger Verfürth Ruhr-Universität Bochum, Germany Self-adaptive discretization methods have gained an enormous importance for the numerical solution of partial differential equations which arise in physical and technical applications. The aim of these methods is to obtain a numerical solution within a prescribed tolerance using a minimal amount of work. The main tools utilised are a posteriori error estimators and indicators which are able to give global and local information on the error of the numerical solution, using only the computed numerical solution and known data of the problem. Presenting the most frequently used error estimators which have been developed by various scientists in the last two decades, this book demonstrates that they are all based on the same basic principles. These principles are then used to develop an abstract framework which is able to handle general nonlinear problems. The abstract results are applied to various classes of nonlinear elliptic partial differential equations from, for example, fluid and continuum mechanics, to yield reliable and easily computable error estimators. The book covers stationary problems but omits transient problems, where theory is often still too complex and not yet well developed.
Functional A Posteriori Error Estimates For Elastic Problems With Nonlinear Boundary Conditions
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Author : Pekka Neittaanmäki
language : en
Publisher:
Release Date : 2011
Functional A Posteriori Error Estimates For Elastic Problems With Nonlinear Boundary Conditions written by Pekka Neittaanmäki and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with categories.
We analyze variational inequalities related to problems in the theory of elasticity that involve unilateral boundary conditions with or without friction. We are focused on deriving upper a posteriori estimates of difference between exact solutions of such type variational inequalities and any functions lying in the admissible functional class of the considered problem. These estimates are obtained by a modification of duality technique earlier used for variational problems with uniformly convex functionals by S. Repin. We also present a simple two dimensional axially symmetric problem with a friction boundary condition and derive an analytical solution. Several numerical tests are performed to demonstrate the quality of our developed estimates.
Adaptive Finite Element Methods For Differential Equations
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Author : Wolfgang Bangerth
language : en
Publisher: Birkhäuser
Release Date : 2013-11-11
Adaptive Finite Element Methods For Differential Equations written by Wolfgang Bangerth and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-11 with Mathematics categories.
These Lecture Notes have been compiled from the material presented by the second author in a lecture series ('Nachdiplomvorlesung') at the Department of Mathematics of the ETH Zurich during the summer term 2002. Concepts of 'self adaptivity' in the numerical solution of differential equations are discussed with emphasis on Galerkin finite element methods. The key issues are a posteriori er ror estimation and automatic mesh adaptation. Besides the traditional approach of energy-norm error control, a new duality-based technique, the Dual Weighted Residual method (or shortly D WR 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. The basics of the DWR method and various of its applications are described in the following survey articles: R. Rannacher [114], Error control in finite element computations. In: Proc. of Summer School Error Control and Adaptivity in Scientific Computing (H. Bulgak and C. Zenger, eds), pp. 247-278. Kluwer Academic Publishers, 1998. M. Braack and R. Rannacher [42], Adaptive finite element methods for low Mach-number flows with chemical reactions.
A Review Of A Posteriori Error Estimation And Adaptive Mesh Refinement Techniques
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Author : Rüdiger Verführt
language : en
Publisher: Springer
Release Date : 1996-07
A Review Of A Posteriori Error Estimation And Adaptive Mesh Refinement Techniques written by Rüdiger Verführt and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-07 with Mathematics categories.
Error Control Adaptive Discretizations And Applications Part 1
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Author :
language : en
Publisher: Elsevier
Release Date : 2024-06-28
Error Control Adaptive Discretizations And Applications Part 1 written by and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-06-28 with Science categories.
Error Control, Adaptive Discretizations, and Applications, Volume 58, Part One highlights new advances in the field, with this new volume presenting interesting chapters written by an international board of authors. Chapters in this release cover hp adaptive Discontinuous Galerkin strategies driven by a posteriori error estimation with application to aeronautical flow problems, An anisotropic mesh adaptation method based on gradient recovery and optimal shape elements, and Model reduction techniques for parametrized nonlinear partial differential equations. Covers multi-scale modeling Includes updates on data-driven modeling Presents the latest information on large deformations of multi-scale materials
Numerical Solution Of Variational Inequalities By Adaptive Finite Elements
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Author : Franz-Theo Suttmeier
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-03-12
Numerical Solution Of Variational Inequalities By Adaptive Finite Elements written by Franz-Theo Suttmeier 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 2009-03-12 with Mathematics categories.
The author presents a general approach to a posteriori error estimation and adaptive mesh design for finite element models where the solution is subjected to inequality constraints. The local weighted residuals, that result from an extension of the so-called Dual-Weighted-Residual method, are used in a feed-back process for generating economical meshes. Based on several model problems, a general concept is proposed, which provides a systematic way of adaptive error control for problems stated in form of variational inequalities.
A Posteriori Estimates For Partial Differential Equations
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Author : Sergey I. Repin
language : en
Publisher: Walter de Gruyter
Release Date : 2008-10-31
A Posteriori Estimates For Partial Differential Equations written by Sergey I. Repin and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-10-31 with Mathematics categories.
This book deals with the reliable verification of the accuracy of approximate solutions which is one of the central problems in modern applied analysis. After giving an overview of the methods developed for models based on partial differential equations, the author derives computable a posteriori error estimates by using methods of the theory of partial differential equations and functional analysis. These estimates are applicable to approximate solutions computed by various methods.