Reliable Methods for Computer Simulation —— Error Control and Posteriori Estimates

----- 计算机模拟的可靠方法：误差控制和后验估计

ISBN: 9780444513762 出版年：2004 页码：317 Neittaanmaki, Pekka Repin, Sergey R Elsevier Science_RM

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