Superconvergence of the gradient for cubic triangular finite elements

Superconvergence of the gradient of approximate solutions to second order elliptic equations is analyzed and justified for the 10-node cubic triangular elements. The existence of superconvergent points is proved. A recovery gradient technique in a subdomain is presented. The superclose property is proved. A rigorous proof of the superconvergent error estimate in a recovered gradient function is obtained. Numerical experiments supporting the theory under study are presented.