caa a22 4500 605523584 CHVBK 20210128100750.0 cr unu---uuuuu 210128e20151101xx s 000 0 eng 10.1007/s10958-015-2588-x doi (NATIONALLICENCE)springer-10.1007/s10958-015-2588-x Estimates of the Distance to the Exact Solution of Parabolic Problems Based on Local Poincaré Type Inequalities [Elektronische Daten] [S. Matculevich, S. Repin] The goal of the paper is to derive two-sided bounds of the distance between the exact solution of the evolutionary reaction-diffusion problem with mixed Dirichlet-Robin boundary conditions and any function in the admissible energy space. The derivation is based upon special transformations of the integral identity that defines the generalized solution. To obtain estimates with easily computable local constants, the classical Poincaré inequalities and Poincaré type inequalities for functions with zero mean boundary traces are exploited. The corresponding constants were estimated earlier. Bounds of the distance to the exact solution contain only these constants associated with subdomains. It is proved that the bounds are equivalent to the energy norm of the error. Bibliography: 15 titles. Springer Science+Business Media New York, 2015 Matculevich S. St.Petersburg Department of the Steklov Mathematical Institute, St. Petersburg, Russia aut Repin S. St.Petersburg Department of the Steklov Mathematical Institute, St. Petersburg, Russia aut Journal of Mathematical Sciences Springer US; http://www.springer-ny.com 210/6(2015-11-01), 759-778 1072-3374 210:6<759 2015 210 10958 https://doi.org/10.1007/s10958-015-2588-x text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10958-015-2588-x text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Matculevich S. St.Petersburg Department of the Steklov Mathematical Institute, St. Petersburg, Russia aut NATIONALLICENCE 700 1- Repin S. St.Petersburg Department of the Steklov Mathematical Institute, St. Petersburg, Russia aut NATIONALLICENCE 773 0- Journal of Mathematical Sciences Springer US; http://www.springer-ny.com 210/6(2015-11-01), 759-778 1072-3374 210:6<759 2015 210 10958