Reliable Methods for Computer Simulation

Reliable Methods for Computer Simulation, 1st Edition

Error Control and Posteriori Estimates

Reliable Methods for Computer Simulation, 1st Edition,Pekka Neittaanmäki,Sergey Repin,ISBN9780444513762


Elsevier Science




225 X 150

Presentation of the main approaches developed for a posteriori error estimation in various problems.

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Key Features

· computable bounds of approximation errors
· checking algorithms
· iteration processes
· finite element methods
· elliptic type problems
· nonlinear variational problems
· variational inequalities


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.


Mathematical modellers, civil engineers, computer scientists, mathematical economists and mathematical biologists.

Pekka Neittaanmäki

Affiliations and Expertise

University of Jyväskylä, Finland

Sergey Repin

Affiliations and Expertise

V.A. Steklov Institute of Mathematics, St. Petersburg, Russian Federation

Reliable Methods for Computer Simulation, 1st Edition

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.

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