Author: Ronald H. W. HoppePublisher:
ISBN:
Category :
Languages : en
Pages :
Book Description
Adaptive Finite Element Methods for Mixed Control-state Constrained Optimal Control Problems for Elliptic Boundary Value Problems
Finite Element Error Analysis for PDE-constrained Optimal Control Problems
Author: Dieter SirchPublisher: Logos Verlag Berlin GmbH
ISBN: 3832525572
Category : Mathematics
Languages : en
Pages : 166
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.
Constrained Optimization and Optimal Control for Partial Differential Equations
Author: Günter LeugeringPublisher: Springer Science & Business Media
ISBN: 3034801335
Category : Mathematics
Languages : en
Pages : 622
Book Description
This special volume focuses on optimization and control of processes governed by partial differential equations. The contributors are mostly participants of the DFG-priority program 1253: Optimization with PDE-constraints which is active since 2006. The book is organized in sections which cover almost the entire spectrum of modern research in this emerging field. Indeed, even though the field of optimal control and optimization for PDE-constrained problems has undergone a dramatic increase of interest during the last four decades, a full theory for nonlinear problems is still lacking. The contributions of this volume, some of which have the character of survey articles, therefore, aim at creating and developing further new ideas for optimization, control and corresponding numerical simulations of systems of possibly coupled nonlinear partial differential equations. The research conducted within this unique network of groups in more than fifteen German universities focuses on novel methods of optimization, control and identification for problems in infinite-dimensional spaces, shape and topology problems, model reduction and adaptivity, discretization concepts and important applications. Besides the theoretical interest, the most prominent question is about the effectiveness of model-based numerical optimization methods for PDEs versus a black-box approach that uses existing codes, often heuristic-based, for optimization.
Issues in Computation: 2011 Edition
Author: Publisher: ScholarlyEditions
ISBN: 146496453X
Category : Computers
Languages : en
Pages : 1318
Book Description
Issues in Computation / 2011 Edition is a ScholarlyEditions™ eBook that delivers timely, authoritative, and comprehensive information about Computation. The editors have built Issues in Computation: 2011 Edition on the vast information databases of ScholarlyNews.™ You can expect the information about Computation in this eBook to be deeper than what you can access anywhere else, as well as consistently reliable, authoritative, informed, and relevant. The content of Issues in Computation / 2011 Edition has been produced by the world’s leading scientists, engineers, analysts, research institutions, and companies. All of the content is from peer-reviewed sources, and all of it is written, assembled, and edited by the editors at ScholarlyEditions™ and available exclusively from us. You now have a source you can cite with authority, confidence, and credibility. More information is available at http://www.ScholarlyEditions.com/.
An Adaptive Finite Element Method for Control-constrained Optimal Control Problems
Author: Kristina KohlsAccuracy Verification Methods
Author: Olli MaliPublisher: Springer Science & Business Media
ISBN: 9400775814
Category : Computers
Languages : en
Pages : 366
Book Description
The importance of accuracy verification methods was understood at the very beginning of the development of numerical analysis. Recent decades have seen a rapid growth of results related to adaptive numerical methods and a posteriori estimates. However, in this important area there often exists a noticeable gap between mathematicians creating the theory and researchers developing applied algorithms that could be used in engineering and scientific computations for guaranteed and efficient error control. The goals of the book are to (1) give a transparent explanation of the underlying mathematical theory in a style accessible not only to advanced numerical analysts but also to engineers and students; (2) present detailed step-by-step algorithms that follow from a theory; (3) discuss their advantages and drawbacks, areas of applicability, give recommendations and examples.
Error-controlled Adaptive Finite Elements in Solid Mechanics
Author: Ekkehard RammPublisher: John Wiley & Sons
ISBN: 0470857978
Category : Technology & Engineering
Languages : en
Pages : 422
Book Description
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
Adaptive Finite Element Methods
Author: Wenbin LiuPublisher: Alpha Science International Limited
ISBN: 9781842657157
Category : Mathematics
Languages : en
Pages : 197
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.
Adaptive Finite Elements for State-constrained Optimal Control Problems - Convergence Analysis and a Posteriori Error Estimation
Author: Simeon SteinigError-controlled Adaptive Finite Elements in Solid Mechanics
Author: Ekkehard RammPublisher: John Wiley & Sons
ISBN: 0471496502
Category : Technology & Engineering
Languages : en
Pages : 436
Book Description
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