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Numerische Mathematik

, Volume 21, Issue 3, pp 270–278 | Cite as

Superconvergence for galerkin methods for the two point boundary problem via local projections

  • Jim DouglasJr.
  • Todd Dupont
Article

Abstract

The two point boundary problemy′'-a(x)y−b(x)y=-f(x), o<x<1,y(0)=y(1)=0, is first solved approximately by the standard Galerkin method, (Y′, υ′) + (aY′+bY, υ)=(f, υ), υ ∈ ℳ 1 0 (r, δ), for a function Y∈ℳ 1 0 (r, δ), the space ofC1-piecewise-ψ-degree-polynomials vanishing atx=0 andx=1 and having knots at {x 0 ,x 1 , ...,x M }=δ. ThenY is projected locally into a polynomial of higher degree by means of one of several projections. It is then shown that higher-order convergence results locally, provided thaty is locally smooth and δ is quasi-uniform.

Keywords

Mathematical Method Point Boundary Boundary Problem Galerkin Method Convergence Result 
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Copyright information

© Springer-Verlag 1973

Authors and Affiliations

  • Jim DouglasJr.
    • 1
  • Todd Dupont
    • 1
  1. 1.University of ChicagoChicagoUSA

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