Higher accuracy using an extrapolation technique for FEM

The boundary value problem for eliptical differential equation of second order was solved by FEM with simplex finite elements. The discrete solution of higher accuracy was obtained using a superposition of proper number of such solutions on different meshes. The parameters of superposed solution were determined using the parameters of the meshes taking a part into superposition. The error estimate in the max-norm depends only on the smoothness of the right hand side function. Some examples are given for superposition of the FEM solutions for six different uniform meshes.