Summary: This paper gives an overview for several two-scaled finite element discretization schemes for a class of elliptic partial differential equations, including both boundary value and eigenvalue problems. These schemes are based on globally and locally coupled discretizations. With these schemes, the solution of a boundary value or eigenvalue problem on a fine grid may be reduced to the solution of a boundary value or eigenvalue problem on a relatively coarse grid and the solutions of linear algebraic systems on several partially fine grids by some parallel procedure. It is shown that this type of discretization schemes not only significantly reduce the number of degrees of freedom but also produce very accurate approximations.