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.