[Studies in Mathematics and Its Applications] Reliable Methods for Computer Simulation - Error Control and A Posteriori Estimates Volume 33 || Chapter 1 Introduction
✍ Scribed by ,
- Book ID
- 121647591
- Publisher
- Elsevier
- Year
- 2004
- Tongue
- English
- Weight
- 269 KB
- Edition
- 1
- Category
- Article
- ISBN
- 0444513760
- ISSN
- 0168-2024
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✦ Synopsis
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