Superconvergence of conforming and nonconforming finite element approximation for elliptic problems by L2-projection

Finite element superconvergence method focuses on approximating the element with an exact solution with a percentage greater than the estimated value of the optimum order error. It is considered as one a great interest due to its very rapid convergence. In this paper, we review the superconvergence in the method of finite elements conforming and nonconforming of elliptical problems of the second degree through arithmetic experiments to show the merits of each of them and using the L2-projection. The results of the presented examples, which were arithmetically solved and represented using Matlab, indicate a great accuracy in the superconvergence of NCFEM and CFEM projections using L2.