Dual analysis for heat conduction problems by finite elements

An alternative approach to the usual finite element treatment of steady-state temperature problems is presented, using approximations for the field of the dual variables. The appropriate extremum principle is established and its minimization is discussed in connection with a plane triangular finite element process. Original heat flow elements are derived: in conjunction with temperature elements, they enable dual analysis of a given structure and an important estimate of the convergence to the true solution by upper and lower bounds to the dissipation function, as illustrated by means of several examples.