Abstract:Combined variation principles can enhance the stability of numerical solution, combined hybrid finite element method of heat transfer equation is built on the basis of the domain decomposition technique. The combined hybrid triangular element, in which the temperature gradient is interpolated by linear polynomials on each element, but the temperature is interpolated by the sum of the linear polynomials and the non-conforming quadratic polynomials, is given. Unlike the combined hybrid rectangular element, only the weighted energy orthogonal relation of the divergence of piecewise linear temperature gradient interpolation and the non-conforming temperature interpolation is given. The stiffness matrix of this element of is equivalent to the conforming triangular linear element, and the non-conforming parts have no contribution to temperature evaluation. At last, the numerical experiments verify the accuracy of the theoretical results.