Abstract: Consider -△u=f in rectangle Ω, u=0 on ∂Ω. Let u_h∈S_h be bilinear Galerkin projection of u. We proved the following:1) superconvergence D_xy²(u-u_h)=0(h²Inh)|u|_4,∞ at center Z_j of each rectangle element τ_j holds; 2) we can construct a piecewise linear contitnuous function w^h by D_xy²u_h and define q_h∈S_h satisfying
(▽q_h,▽v)=-(1)/3(h²+k^-2)(w^h,D_xy²v),v∈S_h;3) correction ũ_h=u_h+q_h are of high accuracy u-ũ_h=0(h⁴|Inh|²)‖u‖_4,∞;4) by ũh the correction derivatives Dũ_h can be got such that Du-Dũ_h=0(h³|In h|²)‖u‖_4,∞.