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
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.