Reliable Methods for Computer Simulation: Error Control and Posteriori Estimates

by Pekka Neittaanmäki, Sergey R. Repin

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.

Product Details

ISBN-13:	9780080540504
Publisher:	Elsevier Science
Publication date:	09/04/2004
Series:	Studies in Mathematics and its Applications , #33
Sold by:	Barnes & Noble
Format:	eBook
Pages:	316
File size:	8 MB

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.