St. Petersburg Polytechnic University Journal: Physics and Mathematics Научно-технические ведомости СПбГПУ. Физико-математические науки 2304-9782, 2618-8686, 2405-7223 16 10.18721/JPM.13416 Functional-type a posteriori error estimates for solutions of problems in deformable solid mechanics Функциональные апостериорные оценки точности решений задач механики деформируемого твердого тела Valdman Jan jan.valdman@gmail.com 0000-0002-1022-0221 Frolov Maxim frolov_me@spbstu.ru University of South Bohemia in České Budejovice Peter the Great St. Petersburg Polytechnic University 28 12 2020 13 4 203 215

The paper provides a historical review and recent developments on theoretical justification and numerical implementations of functional a posteriori error estimates and adaptive algorithms for approximate solutions to problems in deformable solid mechanics. The efficient practical implementation of such methods is a relevant objective, including for modern engineering practice.

 error estimates finite element method adaptive algorithms solid mechanics