Reliable Methods for Computer Simulation: Error Control and Posteriori Estimates Volume 33

ISBN-13: 9780444513762 / Angielski / Twarda / 2004 / 316 str.

Neittaanmaki

Opis

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

Spis treści

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.