Mixed and hybrid non-linear variational analysis of a three dimensional heat conduction problem - Finite element results

The numerical analysis of a nonlinear steady state thermal problem in the nonhomogeneous case of variable conductivities with convection losses and nonlinear boundary conditions is investigated for three-dimensional structures. The equations and corresponding temperature variational formulation of the problem are recalled for the homogeneous case, and the corresponding mixed hybrid nonlinear variational formulation is then established in a general case, using as unknowns the temperature and the heat flux. The coupling between the primal formulation and the mixed hybrid one into a localized region of the structure is then presented. The extension to the nonhomogeneous case is briefly shown, and numerical and experimental results illustrating the accuracy of the present procedure with regard to previously obtained results for the temperature gradient are presented.