
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 Galerkintype 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 wellknown, 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