Details

A Posteriori Error Analysis Via Duality Theory


A Posteriori Error Analysis Via Duality Theory

With Applications in Modeling and Numerical Approximations
Advances in Mechanics and Mathematics, Band 8

von: Weimin Han

142,79 €

Verlag: Springer
Format: PDF
Veröffentl.: 30.07.2006
ISBN/EAN: 9780387235370
Sprache: englisch
Anzahl Seiten: 302

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Beschreibungen

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.
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.
Preliminaries.- Elements of Convex Analysis, Duality Theory.- A Posteriori Error Analysis for Idealizations in Linear Problems.- A Posteriori Error Analysis for Linearizations.- A Posteriori Error Analysis for Some Numerical Procedures.- Error Analysis for Variational Inequalities of the Second Kind.
This volume 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 variational problems. The author avoids giving the results in the most general, abstract form so that it is easier for the reader to understand more clearly the essential ideas involved. Many examples are included to show the usefulness of the derived error estimates.
Audience
This volume is suitable for researchers and graduate students in applied and computational mathematics, and in engineering.
There is no other book of its kind

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