Effectively implementable iterative methods for the linear elliptic variational inequalities with constraints to the gradient of solution

We construct and investigate a new iterative method for a finite dimensional constrained saddle point problem. The obtained results are applied to prove the convergence of different iterative methods for the mesh approximations of variational inequalities with constraints to the gradient of a solution. In particular, we prove the convergence of two-stage iterative methods. The main advantage of the proposed methods is the simplicity of their implementation. The results of the numerical testing demonstrate high convergence rate.