For the enhanced stability of numerical solution, combined hybrid finite element method of heat transfer equation is built based on domain decomposition technique.The combined hybrid rectangular element, in which the temperature gradient is interpolated by linear polynomials on each element, but the temperature is interpolated by the sum of the bilinear polynomials and the Wilson non-conforming quadratic polynomials is given. Unlike in the case of elasticity problem, the weighted energy orthogonal relations between the gradient of non-conforming temperature interpolation and piecewise linear temperature gradient interpolation as well as the divergence of piecewise linear temperature gradient interpolation and the non-conforming temperature interpolation are given respectively.This element of stiffness matrix is equivalent to the conforming rectangular bilinear element,and the non-conforming parts have no contribution to temperature evaluation.

combinative stability; energy orthogonal; enhanced temperature; stiffness matrix