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Functional a posteriori error estimates for elastic problems with nonlinear boundary conditions
Pekka Neittaanäki, Sergey Repin and Jan Valdman
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.