0470507 20240103213532.420170207235959.9 85008199888 000394199100005 10.1016/j.camwa.2016.11.037 14 s. P cav_un_epca*02525590898-1221733 (2017)419-432Elsevier A free boundary problem A posteriori error analysis Finite element method cav_un_auth*0342513 Bozorgnia F. PT 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-0470507.pdf cav_un_auth*0331681 GF16-34894L GA ČR CZ cav_un_auth*0342514 7AMB16AT015 GA MŠk CZ This paper is concerned with the two-phase obstacle problem, a type of a variational free boundary problem. We recall the basic estimates of Repin and Valdman (2015) and verify them numerically on two examples in two space dimensions. A solution algorithm is proposed for the construction of the finite element approximation to the two-phase obstacle problem. The algorithm is not based on the primal (convex and nondifferentiable) energy minimization problem but on a dual maximization problem formulated for Lagrange multipliers. The dual problem is equivalent to a quadratic programming problem with box constraints. The quality of approximations is measured by a functional a posteriori error estimate which provides a guaranteed upper bound of the difference of approximated and exact energies of the primal minimization problem. The majorant functional in the upper bound contains auxiliary variables and it is optimized with respect to them to provide a sharp upper bound. BA 10000 10100 10102 2018 2 4 A hod 4ah 20231122142237.6 RVO:67985556 http://hdl.handle.net/11104/0268129 1 Department of Decision Making Theory UTIA-B 10102 MATHEMATICS, APPLIED S 2 Article Mathematics Applied 2 Article Mathematics Applied 2 Article Mathematics Applied MATHEMATICS.APPLIED 2.080 0.713 7.4 0.01834 0.733 13723 1.058 1.585 408 Q1 58.147 86.7 Q2 Q2 1.38 Q1 86.706 2017 Soubory v repozitáři: valdman-0470507.pdf 85008199888 SCOPUS PUBMED 000394199100005 WOS cav_un_epca*0252559 Computers & Mathematics With Applications 0898-1221 1873-7668 Roč. 73 č. 3 2017 419 432 Elsevier