This paper presents a new robust multigrid technique for solving boundary value problems in a black box manner. To overcome the problem of robustness, the technique is based on the incorporation of adaptation of boundary value problems to numerical methods, control volume discretization and a new multigrid solver into a united computational algorithm. The special multiple coarse grid correction strategy makes it possible to obtain problem-independent transfer operators. As a result, most modes are approximated on coarse grids to make the task of the smoother on the finest grid the least demanding. A detailed description of the robust multigrid technique and examples of its application for solving benchmark problems are given in the paper.