Superconvergence in high-order Galerkin finite element methods Original Research Article

In this paper, we shall use local estimates to give the superconvergence of high-order Galerkin finite element method for the elliptic equation of second order with constant coefficients by using the symmetric technique and integral identity. We get improved superconvergence on the inner locally symmetric mesh with respect to a point x0 for rectangular and triangular meshes.