In this paper, an improved method of studying superconvergence and extrapola-tion is presented, whose key point is to obtain superconvergence and extrapolationof u - uh at locally symmetric points by investigating superconvergence and ex-trapolation of uI - uh at locally symmetric points. Using this method, for 2-ordertriangular element, following estimation is discovered:where u*=4uh-u2h/3 0＜e＜1, X is a local symmetric point of Ω, and for p-orderrectiangular element, there exists:|(u - uh)(X)| ≤ chp+3| ln |ln |ln h|||||u||p+4,owhere X is a vertex of local symmetry and p = 2k(k ∈ N, k ≥ 2).
