By
Pekka Neittaanmäki, University of Jyväskylä, Finland
Sergey Repin, V.A. Steklov Institute of Mathematics, St. Petersburg, Russian Federation
Description
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.
Included in series
Studies in Mathematics and its Applications
Audience:
Mathematical modellers, civil engineers, computer scientists, mathematical economists and mathematical biologists.
