SUPERCONVERGENCE FOR L~2-PROJECTION IN FINITE ELEMENTS

Consider L~2-projection u_h of u to n-degree finite element space on one-dimensional uniform grids. Two different classes of the orthogonal expansion in an element for constructing a superclose to function u_h are proposed and then superconvergence for both u_h and Du_h are proved. When n is odd and no boundary conditions are prescribed, then u_h is of superconvergence at n+1 order Gauss points G_(n+1) in each element. When n is even and function values on the boundary are prescribed, then u_h is of superconvergence at n+1 order points Z_(n+1) in each element. If the other boundary conditions are given, then the conclusions are valid in all elements that its distance from the boundary≥ch|lnh|. The above conclusions are also valid. for n-dergree rectangular element Q_1 (n).

SUPERCONVERGENCE FOR L~2-PROJECTION IN FINITE ELEMENTS