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# Reliable Methods for Computer Simulation, Vol 33. Studies in Mathematics and its Applications

• ID: 1762884
• Book
• September 2004
• 316 Pages
• Elsevier Science and Technology

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

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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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Neittaanmäki, Pekka
Pekka Neittaanmäki is Professor at University of Jyväskylä and the UNESCO Chair on Digital Platforms for Emerging Economies. He is the author of 50 books and 300 articles. He is on the Board of 10 journals and academic associations and has received 10 honorable awards. His research is on digital platform economics and information technology industrial applications.
Repin, Sergey R.
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