Reliable Methods for Computer Simulation: Error Control and Posteriori Estimates

Reliable Methods for Computer Simulation: Error Control and Posteriori Estimates

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by Pekka Neittaanmaki, S. Repin, Sergey R. Repin
     
 

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ISBN-10: 0444513760

ISBN-13: 9780444513762

Pub. Date: 08/08/2004

Publisher: Elsevier Science

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

Overview

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

Product Details

ISBN-13:
9780444513762
Publisher:
Elsevier Science
Publication date:
08/08/2004
Series:
Studies in Mathematics and its Applications Series, #33
Pages:
316
Product dimensions:
0.75(w) x 6.14(h) x 9.21(d)

Table of Contents

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.

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Reliable Methods for Computer Simulation: Error Control and Posteriori Estimates 5 out of 5 based on 0 ratings. 1 reviews.
Anonymous More than 1 year ago
Wanna hear about yesterday.