Reliable methods for computer simulation error control and a posteriori estimates
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 reliab...
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| Format: | eBook |
| Language: | English |
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Amsterdam
Elsevier
2004, 2004
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| Series: | Studies in mathematics and its applications
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| Collection: | Elsevier eBook collection Mathematics - Collection details see MPG.ReNa |
| Summary: | 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 |
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| Physical Description: | x, 305 pages illustrations |
| ISBN: | 9780080540504 1435601017 9780444513762 0080540503 9781281019080 9786611019082 0444513760 1281019089 9781435601017 |