Numerical verification of solutions for variational inequalities of the second kind

The purpose of this paper is to present an approach to the numerical proof of existence of solutions for the problem of the flow of a viscous plastic fluid in a pipe. Using the finite element approximations and the explicit a priori error estimates for the problem of the flow of a viscous plastic fluid in a pipe, we present an effective verification procedure that, through numerical computation, generates a set which includes the exact solution. Further, a numerical example is presented.