Functional a posteriori estimates for elliptic variational inequalities

In the paper, we present a new way of the derivation of computable estimates for the difference between exact solutions of elliptic variational inequalities and arbitrary functions in the respective energy space that satisfy the main (Dirichlét) boundary conditions. Unlike the method exposed in [11, 18], we derive the estimates by certain transformations of variational inequalities without the attraction of duality arguments. For linear elliptic and parabolic problems this method was suggested in [16, 17]. In the present paper, we consider two different types of variational inequalities (also called variational inequalities of the first and second kinds [10]). The techniques discussed can be applied to other nonlinear problems related to variational inequalities.