

Preprint 13/2011
Functional a posteriori error estimates for elastic problems with nonlinear boundary conditions
Pekka Neittaanäki, Sergey Repin, and Jan Valdman
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Submission date: 04. Apr. 2011 (revised version: June 2011)
Pages: 28
Bibtex
Keywords and phrases: a posteriori error estimates, friction boundary condtions
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Abstract:
We analyze variational inequalities related to problems in the theory of elasticity that
involve unilateral boundary conditions with or without friction. We are focused on deriving upper
a posteriori estimates of difference between exact solutions of such type variational inequalities and
any functions lying in the admissible functional class of the considered problem. These estimates
are obtained by a modification of duality technique earlier used for variational problems with
uniformly convex functionals by S. Repin. We also present a simple two dimensional axially
symmetric problem with a friction boundary condition and derive an analytical solution. Several
numerical tests are performed to demonstrate the quality of our developed estimates.