Reliable Methods for Computer Simulation
Error Control and Posteriori Estimates
Nonfiction, Computers, Advanced Computing, Engineering, Computer Engineering, Science & Nature, Mathematics, General Computing
| Author: | Pekka Neittaanmäki, Sergey R. Repin | ISBN: | 9780080540504 |
| Publisher: | Elsevier Science | Publication: | September 4, 2004 |
| Imprint: | Elsevier Science | Language: | English |
| Author: | Pekka Neittaanmäki, Sergey R. Repin |
| ISBN: | 9780080540504 |
| Publisher: | Elsevier Science |
| Publication: | September 4, 2004 |
| Imprint: | Elsevier Science |
| Language: | English |
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
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
