6533b86ffe1ef96bd12cdb77

RESEARCH PRODUCT

Overview of Other Results and Open Problems

Sergey RepinSergey RepinOlli MaliPekka Neittaanmäki

subject

Nonlinear systemComputer scienceIterative methodSection (archaeology)Variational inequalityCalculusA priori and a posterioriSubject (documents)Estimation methodsError detection and correction

description

This chapter presents an overview of results related to error control methods, which were not considered in previous chapters. In the first part, we discuss possible extensions of the theory exposed in Chaps. 3 and 4 to nonconforming approximations and certain classes of nonlinear problems. Also, we shortly discuss some results related to explicit evaluation of modeling errors. The remaining part of the chapter is devoted to a posteriori estimates of errors in iteration methods. Certainly, the overview is not complete. A posteriori error estimation methods are far from having been fully explored and this subject contains many unsolved problems and open questions, some of which we formulate in the last section.

yearjournalcountryeditionlanguage
2014-01-01
https://doi.org/10.1007/978-94-007-7581-7_6