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)

Document Details

Document Type
Technical Report
Publication Date
Sep 01, 1969
Accession Number
AD0713434

Entities

People

  • Hermann G. Burchard
  • Jean Pierre Aubin

Organizations

  • University of Wisconsin–Madison

Tags

DTIC Thesaurus Topics

  • Boundaries
  • Boundary Value Problems
  • Convergence
  • Differential Equations
  • Equations
  • Mathematical Analysis
  • Mathematics

Fields of Study

  • Mathematics

Readers

  • Computational Linguistics
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Operations Research

Technology Areas

  • Space