Functional A Posteriori Error Estimates of Elasticity Problems with Nonlinear Boundary Conditions

Prof. Dr. Jan Valdman

April 29, 2011, 1:45 p.m. HF 9904

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 analytical solution. Several numerical tests are performed to demonstrate the quality of our developed estimates.