Application of Hermitian biquadratic finite element

A new type of Hermitian finite element on rectangle is presented which is intermediate between bilinear and bicubic finite elements. The use of this biquadratic element gives less number of unknowns and equations of discrete algebraic systems in comparison with the Lagrangian element of the same degree. The theoretical conclusion of its effectiveness is illustrated by using this finite element for solving boundary value problem for second-order elliptic equation where the second order of accuracy was achieved for approximate solution in the energy norm and the fourth order of accuracy in mean-value norm on uniform mesh.