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Reliable Methods for Computer Simulation, Vol 33. Studies in Mathematics and its Applications

  • ID: 1762884
  • Book
  • 316 Pages
  • Elsevier Science and Technology
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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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1. Introduction.

2. Mathematical background.

3. A posteriori estimates for iteration methods.

4. A posteriori estimates for finite element approximations.

5. Foundations of duality theory.

6. Two-sided a posteriori estimates for linear elliptic problems.

7. A posteriori estimates for nonlinear variational problems.

8. A posteriori estimates for variational inequalities.

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Neittaanmäki, Pekka
Repin, Sergey R.
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