- The concept of conjugate approximation functions is generalized to mixed formulations of linear boundary value problems. Biorthogonal basis functions are generated using two distinct finite-element models of the domain of a given function. Various special cases are considered. It is shown that four distinct models can be developed corresponding to a single linear operator. A comparison of the concepts of the hypercircle and conjugate approximation is given. 1972, Taylor & Francis Group, LLC. All rights reserved.