Numerical Solution Of Variational Inequalities By Adaptive Finite Elements
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Numerical Solution Of Variational Inequalities By Adaptive Finite Elements
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Author : Franz-Theo Suttmeier
language : de
Publisher:
Release Date : 2006
Numerical Solution Of Variational Inequalities By Adaptive Finite Elements written by Franz-Theo Suttmeier and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with categories.
Adaptive Finite Element Methods For Variational Inequalities
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Author : B. Erdmann
language : en
Publisher:
Release Date : 1993
Adaptive Finite Element Methods For Variational Inequalities written by B. Erdmann and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Boundary value problems categories.
Abstract: "In this paper we are concerned with the numerical solution of stationary variational inequalities of obstacle type associated with second order elliptic differential operators in two or three space dimensions. In particular, we present adaptive finite element techniques featuring multilevel iterative solvers and a posteriori error estimators for local refinement of the triangulations. The algorithms rely on an outer-inner iterative scheme with an outer active set strategy and inner multilevel preconditioned cg-iterations involving variants of the hierarchical and the BPX-preconditioner which are derivded [sic] in the framework of multilevel additive Schwarz iterations. For the a posteriori error estimation in the energy norm three error estimators are presented which are based on the approximate solution of a quasivariational inequality satisfied by a piecewise quadratic approximation of the global discretization error. Finally, the performance of the preconditioners and the error estimators is illustrated by numerical results for a wide variety of stationary free boundary problems."
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.
Adaptive Monotone Multigrid Methods For Nonlinear Variational Problems
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Author : Ralf Kornhuber
language : en
Publisher:
Release Date : 1997
Adaptive Monotone Multigrid Methods For Nonlinear Variational Problems written by Ralf Kornhuber and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Mathematics categories.
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.
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.
Adaptive Finite Element Methods For Variational Inequalities
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Author : Chen-Song Zhang
language : en
Publisher:
Release Date : 2007
Adaptive Finite Element Methods For Variational Inequalities written by Chen-Song Zhang 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.
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.
A Posteriori Error Analysis And Adaptive Finite Element Solution Of Variational Inequalities Of The Second Kind
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Author : Viorel Bostan
language : en
Publisher:
Release Date : 2004
A Posteriori Error Analysis And Adaptive Finite Element Solution Of Variational Inequalities Of The Second Kind written by Viorel Bostan and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with categories.
Finite Element Method For Hemivariational Inequalities
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Author : J. Haslinger
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Finite Element Method For Hemivariational Inequalities written by J. Haslinger 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 2013-03-09 with Mathematics categories.
Hemivariational inequalities represent an important class of problems in nonsmooth and nonconvex mechanics. By means of them, problems with nonmonotone, possibly multivalued, constitutive laws can be formulated, mathematically analyzed and finally numerically solved. The present book gives a rigorous analysis of finite element approximation for a class of hemivariational inequalities of elliptic and parabolic type. Finite element models are described and their convergence properties are established. Discretized models are numerically treated as nonconvex and nonsmooth optimization problems. The book includes a comprehensive description of typical representants of nonsmooth optimization methods. Basic knowledge of finite element mathematics, functional and nonsmooth analysis is needed. The book is self-contained, and all necessary results from these disciplines are summarized in the introductory chapter. Audience: Engineers and applied mathematicians at universities and working in industry. Also graduate-level students in advanced nonlinear computational mechanics, mathematics of finite elements and approximation theory. Chapter 1 includes the necessary prerequisite materials.