Estimates of deviations from exact solutions for elasticity problems with nonlinear boundary conditions

Abstract

We present a method of deriving fully guaranteed bounds of the difference between the exact and approximate solutions of variational inequalities generated by problems in the theory of elasticity with nonlinear boundary conditions (e.g., unilateral and friction type boundary conditions). These estimates are obtained with the help of the duality technique in the calculus of variations. They do not contain mesh-dependent constants and are valid for any function from the corresponding energy space compared with the exact solution. We prove that the majorants of deviations are continuous and vanish if and only if approximate solutions coincide with the exact one. Several numerical tests demonstrate the quality of the estimates.