0483574 - ÚTIA 2019 RIV DE eng J - Článek v odborném periodiku
Repin, S. - Valdman, Jan
Error identities for variational problems with obstacles.
ZAMM-Zeitschrift fur Angewandte Mathematik und Mechanik. Roč. 98, č. 4 (2018), s. 635-658. ISSN 0044-2267. E-ISSN 1521-4001
Grant CEP: GA ČR(CZ) GF16-34894L; GA ČR GA17-04301S; GA MŠMT(CZ) 7AMB16AT015
Institucionální podpora: RVO:67985556
Klíčová slova: variational problems with obstacles * coincidence set * convex functionals * error identities
Obor OECD: Pure mathematics
Impakt faktor: 1.467, rok: 2018 ; AIS: 0.469, rok: 2018
Web výsledku:
http://library.utia.cas.cz/separaty/2017/MTR/valdman-0483574.pdf

DOI: https://doi.org/10.1002/zamm.201700105

The paper is devoted to analysis of a class of nonlinear free boundary problems that are usually solved by variational methods based on primal, dual or primal-dual variational settings. We deduce and investigate special relations (error identities). They show that a certain nonlinear measure of the distance to the exact solution (specific for each problem) is equivalent to the respective duality gap, whose minimization is the keystone of all variational numerical methods. Therefore, the identity actually sets the measure that contains maximal quantitative information on the quality of a numerical solution available through these methods.
Trvalý link: http://hdl.handle.net/11104/0278827