A posteriori estimates for iteration methods.
A posteriori estimates for finite element approximations.
Foundations of duality theory.
Two-sided a posteriori estimates for linear elliptic problems.
A posteriori estimates for nonlinear variational problems.
A posteriori estimates for variational inequalities.
Bibliography. Notation. Index.
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
Mathematical modellers, civil engineers, computer scientists, mathematical economists and mathematical biologists.
- No. of pages:
- © Elsevier Science 2004
- 25th July 2004
- Elsevier Science
- eBook ISBN:
- Hardcover ISBN:
University of Jyväskylä, Finland
V.A. Steklov Institute of Mathematics, St. Petersburg, Russian Federation