Accuracy comparisons for variational R, T and T^-1 response matrix formulations

Three classes of response matrix methods designated by Lindahl and Weiss (1981) as R, T and T^-1 are formulated variationally using modified forms of the same diffusion theory functional. With polynomial trial functions of identical form, 1-D model problems are solved and compared with exact analytical solutions. The T^-1 formalism which has been shown elsewhere to enforce nodal balance gives superior results. The T formulation, in which essential boundary conditions decrease the available degrees of freedom in the trial function, yields the least accurate results.