Some superconvergence results of high-degree finite element method for a second order elliptic equation with variable coefficients

In this paper, some superconvergence results of high-degree finite element method are obtained for solving a second order elliptic equation with variable coefficients on the inner locally symmetric mesh with respect to a point x (0) for triangular meshes. By using of the weak estimates and local symmetric technique, we obtain improved discretization errors of O(h (p+1) |ln h|(2)) and O(h (p+2) |ln h|(2)) when p (a parts per thousand yen 3) is odd and p (a parts per thousand yen 4) is even, respectively. Meanwhile, the results show that the combination of the weak estimates and local symmetric technique is also effective for superconvergence analysis of the second order elliptic equation with variable coefficients.