SOME ASPECTS OF THE METHOD OF THE HYPERCIRCLE APPLIED TO ELLIPTIC VARIATIONAL PROBLEMS.

Abstract : The hypercircle method is studied from the point of view of the recently developing theory of Galerkin-type approximations in Sobolev spaces using spline functions. Given an elliptic boundary value problem it is shown how to obtain a conjugate problem - thereby interchanging the roles of 'forced' and 'natural boundary conditions. Given approximate solutions for both problems their errors can be estimated 'a posteriori'. The approximate solution of the primal problem being well-known, the authors consider the approximation of the solution of the conjugate problem, obtaining theorems of convergence and estimates of the rate of convergence. (Author)