SOME ASPECTS OF THE METHOD OF THE HYPERCIRCLE APPLIED TO ELLIPTIC VARIATIONAL PROBLEMS.
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WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER
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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
- Theoretical Mathematics