Accession Number : AD0713434

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

Descriptive Note : Technical summary rept.,

Corporate Author : WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER

Personal Author(s) : Aubin,Jean Pierre ; Burchard,Hermann G.

Report Date : SEP 1969

Pagination or Media Count : 76

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)

Descriptors :   (*PARTIAL DIFFERENTIAL EQUATIONS, NUMERICAL INTEGRATION), (*BOUNDARY VALUE PROBLEMS, APPROXIMATION(MATHEMATICS)), NUMERICAL ANALYSIS, DIFFERENCE EQUATIONS, HILBERT SPACE, THEOREMS

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE