CORRECTION OF BILINEAR FINITE-ELEMENT

Consider - DELTA-u = f in rectangle OMEGA, u = 0 on partial-OMEGA. Let u(h) is-a-member-of S(h) be bilinear Galerkin projection of u. We proved the following: 1) superconvergence D(xy)2(u-u(h)) = 0(h2lnh) parallel-to u parallel-to 4, infinity at center Z(i) of each rectangle element tau-j holds; 2) we can construct a piecewise linear contitnuous function w(h) by D(xy)2u(h) and define q(h) is-a-member-of S(h) satisfying (DELTA-q(h), DELTA-v) = -1/3(h2+k2)(w(h), D(xy)2v), for-all v is-a-member-of S(h); 3) correction u approximately h = u(h)+q(h) are of high accuracy u - u approximately h = 0(h4\lnh\2) parallel-to u parallel-to 4, infinity; 4) by u approximately h the correction derivatives D approximately u approximately h can be got such that Du - D approximately u approximately h = 0(h3\ln h\2) parallel-to u parallel-to 4, infinity.