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Book 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.
computable bounds of approximation errors
checking algorithms
iteration processes
finite element methods
elliptic type problems
nonlinear variational problems
variational inequalities
Reliable Methods for Computer Simulation, Volume 33: Error Control and Posteriori Estimates (Studies in Mathematics and its Applications),Pekka Neittaanmäki,Sergey Repin,Elsevier Science,0444513760,Applied,Computer Books: General,Computer Science,Computer Simulation,Computers,Mathematics,Mathematics / Mathematical Analysis
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