0483574 20240103215222.020171220235959.9 85041107421 000430013600010 10.1002/zamm.201700105 24 s. P cav_un_epca*02577150044-2267984 (2018)635-658Wiley variational problems with obstacles coincidence set convex functionals error identities cav_un_auth*0316845 Repin S. RU cav_un_auth*0292941 Valdman Jan Matematická teorie rozhodování Department of Decision Making Theory MTR MTR UTIA-B Department of Decision Making Theory Ústav teorie informace a automatizace AV ČR, v. v. i. http://library.utia.cas.cz/separaty/2017/MTR/valdman-0483574.pdf cav_un_auth*0331681 GF16-34894L GA ČR CZ cav_un_auth*0347023 GA17-04301S GA ČR cav_un_auth*0342514 7AMB16AT015 GA MŠk CZ 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. BA 10000 10100 10101 2019 RVO:67985556 http://hdl.handle.net/11104/0278827 S 3+4 Article Mathematics Applied|Mechanics MECHANICS|MATHEMATICS.APPLIED 1.351 0.467 23.1 0.0028 0.469 2940 0.590 1.379 120 Q2 29.762 49.7 Q3 Q2 0.74 Q2 69.094 2018 85041107421 SCOPUS PUBMED 000430013600010 WOS cav_un_epca*0257715 ZAMM-Zeitschrift fur Angewandte Mathematik und Mechanik 0044-2267 1521-4001 Roč. 98 č. 4 2018 635 658 Wiley