Guaranteed and computable bounds of approximation errors for the semi-discrete Biot problem
Dr. Svetlana MatculevichOct. 2, 2018, 3:30 p.m. S2 054
The talk is concerned with guaranteed and fully computable a posteriori error estimates for evolutionary
problems associated with the poroelastic media governed by the quasi-static linear Biot
equations . It addresses the question of approximation error control, which arises in the iterative
and monolithic approaches used for semi-discrete approximations obtained by the implicit Euler
time-discretization scheme. The derivation of the error bounds is based on a combination of the
Ostrowski-type estimates  derived for iterative schemes and a posteriori error estimates of the
functional type for elliptic problems originally (also called error majorants and minorants) introduced
in . The validity of the first estimates is based on the contraction property of the fixed
stress splitting scheme  used for decoupling. The talk is based on the report .
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applied physics, 26:182–185, 195.
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Acad.Sci. Paris Sér. A–B, 275:A275–A278, 1972.
 S. Repin. A posteriori error estimation for variational problems with uniformly convex functionals.
Math. Comput., 69(230):481–500, 2000.
 A. Mikeli´c and M. F. Wheeler. Convergence of iterative coupling for coupled flow and geomechanics.
Comput. Geosci., 17(3):455–461, 2013.
 Kundan Kumar, Svetlana Matculevich, Jan Nordbotten, and Sergey Repin. Guaranteed
and computable bounds of approximation errors for the semi-discrete Biot problem.