M.E. Frolov | Error control for problems in Cosserat (micropolar) elasticity theory
Channel: EIMI, PDMI RAS and Chebyshev Laboratory
Date: 2022-08-01

O.A. Ladyzhenskaya centennial conference on PDE’s, St. Petersburg, July 16 – July 22, 2022
Maksim E. Frolov (Peter the Great St. Petersburg Polytechnic University) 
Error control for problems in Cosserat (micropolar) elasticity theory

A posteriori error estimates for Cosserat (micropolar) elasticity for problems
in 2D ([2, 3]) and 3D ([4]) are considered. Majorants are based on the  functional approach that guarantees the reliability property regardless of some additional assumptions, for instance, the Galerkin orthogonality (see [5, 6, 7] and the literature cited therein). Error estimates with such type of properties are as important for justification of mathematical methods in computational mechanics as well-known classical results on existence and uniqueness of solutions following from the theory of partial differential equations (see, for example, [1]). 
References
[1] O. A. Ladyzhenskaya, Boundary Value Prolems of Mathematical Physics,
Nauka, Moscow, 1973.
[2] S.I. Repin and M.E. Frolov, Estimates for deviations from exact solutions to plane problems in the Cosserat theory of elasticity, Probl. Math. Anal. 62
(2011), 153–161 [transl. Journal of Mathematical Sciences 181 (2012), no.2,
281–291].
[3] M.E. Frolov, Functional a posteriori estimates of the error in the solutions of plane problems in Cosserat elasticity theory, Journal of Applied Mathematics and Mechanics 78 (2014), no.4, 425–431.
[4] M.E. Frolov, Reliable a Posteriori Error Estimation for Cosserat Elasticity
in 3D, Lobachevskii J. Math. 42 (2021), 96–103.
[5] P. Neittaanm¨aki and S. Repin, Reliable methods for computer simulation.
Error control and a posteriori estimates, Studies in Mathematics and its
Applications, Vol. 33, Elsevier, Amsterdam, 2004.
[6] S. Repin, A posteriori estimates for partial differential equations, Radon
series on computational and applied mathematics, Vol. 4, de Gruyter, Berlin,
2008.
[7] O. Mali, P. Neittaanm¨aki and S. Repin, Accuracy verification methods. Theory and algorithms, Springer, Dordrecht, 2014.