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Reliable methods for computer simula...

Neittaanm�aki, P.

Reliable methods for computer simulationerror control and a posteriori estimates /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Reliable methods for computer simulationP. Neittaanm�aki and S. Repin.
Reminder of title:	error control and a posteriori estimates /
Author:	Neittaanm�aki, P.
other author:	Repin, Sergey I.
Published:	Amsterdam ;Elsevier,2004.
Description:	x, 305 p. :ill. ;24 cm.
Series:	Studies in mathematics and its applications ;
Subject:	Numerical analysis.
Online resource:	An electronic book accessible through the World Wide Web; click for information
Online resource:	http://www.loc.gov/catdir/toc/fy0710/2006277839.html
Online resource:	http://www.loc.gov/catdir/enhancements/fy0665/2006277839-d.html
ISBN:	9780444513762

Reliable methods for computer simulationerror control and a posteriori estimates /
Neittaanm�aki, P.

Reliable methods for computer simulationerror control and a posteriori estimates /[electronic resource] :P. Neittaanm�aki and S. Repin. - Amsterdam ;Elsevier,2004. - x, 305 p. :ill. ;24 cm. - Studies in mathematics and its applications ;v. 33.

Includes bibliographical references (p. 281-299) and index.

Contents -- 1. Introduction. -- 2. Mathematical background. -- 3. A posteriori estimates for iteration methods. -- 4. A posteriori estimates for finite element approximations. -- 5. Foundations of duality theory. -- 6. Two-sided a posteriori estimates for linear elliptic problems. -- 7. A posteriori estimates for nonlinear variational problems. -- 8. A posteriori estimates for variational inequalities. -- Bibliography. -- Notation. -- Index.

Recent decades have seen a very rapid success in developing numerical methods based on explicit control over approximation errors. It may be said that nowadays a new direction is forming in numerical analysis, the main goal of which is to develop methods ofreliable computations. In general, a reliable numerical method must solve two basic problems: (a) generate a sequence of approximations that converges to a solution and (b) verify the accuracy of these approximations. A computer code for such a method must consist of two respective blocks: solver and checker. In this book, we are chiefly concerned with the problem (b) and try to present the main approaches developed for a posteriori error estimation in various problems. The authors try to retain a rigorous mathematical style, however, proofs are constructive whenever possible and additional mathematical knowledge is presented when necessary. The book contains a number of new mathematical results and lists a posteriori error estimation methods that have been developed in the very recent time. computable bounds of approximation errors checking algorithms iteration processes finite element methods elliptic type problems nonlinear variational problems variational inequalities.

Electronic reproduction.
Amsterdam :
Elsevier Science & Technology,
2007.

Mode of access: World Wide Web.

ISBN: 9780444513762

Source: 107980:108022Elsevier Science & Technologyhttp://www.sciencedirect.comSubjects--Topical Terms:

182073
Numerical analysis.
Index Terms--Genre/Form:

214472
Electronic books.

LC Class. No.: QA297.5 / .N45 2004eb

Dewey Class. No.: 003.3

Reliable methods for computer simulationerror control and a posteriori estimates /
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035 $a ocn162130136
037 $a 107980:108022 $b Elsevier Science & Technology $n http://www.sciencedirect.com
040 $a OPELS $c OPELS $d OCLCG
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100 1 $a Neittaanm�aki, P. $q (Pekka) $3 455099
245 1 0 $a Reliable methods for computer simulation $h [electronic resource] : $b error control and a posteriori estimates / $c P. Neittaanm�aki and S. Repin.
260 $a Amsterdam ; $a San Diego, CA : $b Elsevier, $c 2004.
300 $a x, 305 p. : $b ill. ; $c 24 cm.
440 0 $a Studies in mathematics and its applications ; $v v. 33
504 $a Includes bibliographical references (p. 281-299) and index.
505 0 $a Contents -- 1. Introduction. -- 2. Mathematical background. -- 3. A posteriori estimates for iteration methods. -- 4. A posteriori estimates for finite element approximations. -- 5. Foundations of duality theory. -- 6. Two-sided a posteriori estimates for linear elliptic problems. -- 7. A posteriori estimates for nonlinear variational problems. -- 8. A posteriori estimates for variational inequalities. -- Bibliography. -- Notation. -- Index.
520 $a Recent decades have seen a very rapid success in developing numerical methods based on explicit control over approximation errors. It may be said that nowadays a new direction is forming in numerical analysis, the main goal of which is to develop methods ofreliable computations. In general, a reliable numerical method must solve two basic problems: (a) generate a sequence of approximations that converges to a solution and (b) verify the accuracy of these approximations. A computer code for such a method must consist of two respective blocks: solver and checker. In this book, we are chiefly concerned with the problem (b) and try to present the main approaches developed for a posteriori error estimation in various problems. The authors try to retain a rigorous mathematical style, however, proofs are constructive whenever possible and additional mathematical knowledge is presented when necessary. The book contains a number of new mathematical results and lists a posteriori error estimation methods that have been developed in the very recent time. computable bounds of approximation errors checking algorithms iteration processes finite element methods elliptic type problems nonlinear variational problems variational inequalities.
533 $a Electronic reproduction. $b Amsterdam : $c Elsevier Science & Technology, $d 2007. $n Mode of access: World Wide Web. $n System requirements: Web browser. $n Title from title screen (viewed on July 25, 2007). $n Access may be restricted to users at subscribing institutions.
650 0 $a Numerical analysis. $3 182073
650 0 $a Error-correcting codes (Information theory) $3 184310
650 0 $a Approximation theory. $3 185327
655 7 $a Electronic books. $2 local. $3 214472
700 1 $a Repin, Sergey I. $3 455100
710 2 $a ScienceDirect (Online service) $3 307425
776 1 $c Original $z 0444513760 $z 9780444513762 $w (DLC) 2006277839 $w (OCoLC)56463686
856 4 0 $3 ScienceDirect $u http://www.sciencedirect.com/science/publication?issn=01682024&volume=33 $z An electronic book accessible through the World Wide Web; click for information
856 4 1 $3 Table of contents only $u http://www.loc.gov/catdir/toc/fy0710/2006277839.html
856 4 2 $3 Publisher description $u http://www.loc.gov/catdir/enhancements/fy0665/2006277839-d.html
994 $a C0 $b TEF

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