說明 
x, 305 p. : ill. ; 24 cm 

Elsevier 
系列 
Studies in mathematics and its applications ; v. 33

附註 
Includes bibliographical references (p. 281299) 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. Twosided 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 

Electronic reproduction. Amsterdam : Elsevier Science & Technology, 2007. Mode of access: World Wide Web. System requirements: Web browser. Title from title screen (viewed on July 25, 2007). Access may be restricted to users at subscribing institutions 

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 

Elsevier 
鏈接 
Original 0444513760
9780444513762
(DLC) 2006277839 (OCoLC)56463686

主題 
Numerical analysis


Errorcorrecting codes (Information theory)


Approximation theory


Electronic books. local

Alt Author 
Repin, Sergey I


ScienceDirect (Online service)

