Finite Element Error Analysis for State Constrained Optimal Control of the Stokes Equations PDF Download
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Author: Juan Carlos de los Reyes
Publisher:
ISBN:
Category :
Languages : en
Pages : 21
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Book Description
Author: Juan Carlos de los Reyes
Publisher:
ISBN:
Category :
Languages : en
Pages : 21
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Author: Dieter Sirch
Publisher: Logos Verlag Berlin GmbH
ISBN: 3832525572
Category : Mathematics
Languages : en
Pages : 166
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Book Description
Subject of this work is the analysis of numerical methods for the solution of optimal control problems governed by elliptic partial differential equations. Such problems arise, if one does not only want to simulate technical or physical processes but also wants to optimize them with the help of one or more influence variables. In many practical applications these influence variables, so called controls, cannot be chosen arbitrarily, but have to fulfill certain inequality constraints. The numerical treatment of such control constrained optimal control problems requires a discretization of the underlying infinite dimensional function spaces. To guarantee the quality of the numerical solution one has to estimate and to quantify the resulting approximation errors. In this thesis a priori error estimates for finite element discretizations are proved in case of corners or edges in the underlying domain and nonsmooth coefficients in the partial differential equation. These facts influence the regularity properties of the solution and require adapted meshes to get optimal convergence rates. Isotropic and anisotropic refinement strategies are given and error estimates in polygonal and prismatic domains are proved. The theoretical results are confirmed by numerical tests.
Author: Jangwoon Lee
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Author: Lisheng Hou
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Author: Roland Becker
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Author: Roland Becker
Publisher:
ISBN:
Category :
Languages : en
Pages : 14
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Book Description
Navier-Stokes equations, finite elements, a posteriori error estimates, mesh adaptation.
Author: Wenbin Liu
Publisher: Alpha Science International Limited
ISBN: 9781842657157
Category : Mathematics
Languages : en
Pages : 197
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Book Description
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.
Author: Hongchul Kim
Publisher:
ISBN:
Category : Navier-Stokes equations
Languages : en
Pages : 304
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Author: Vivette Girault
Publisher:
ISBN: 9783662197356
Category :
Languages : en
Pages : 220
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Author: Wolfgang Bangerth
Publisher: Springer Science & Business Media
ISBN: 9783764370091
Category : Mathematics
Languages : en
Pages : 222
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Book Description
The key issues are a posteriori error estimation and it automatic mesh adaptation. Besides the traditional approach of energy-norm error control, a new duality-based technique, the Dual Weighted Residual 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. At the end of each chapter some exercises are posed in order to assist the interested reader in better understanding the concepts presented. Solutions and accompanying remarks are given in the Appendix.
