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

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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 01 (r, δ), for a function Y∈ℳ 01 (r, δ), the space ofC 1-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.

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References

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Authors and Affiliations

  1. University of Chicago, 60637, Chicago, Illinois, USA

    Jim Douglas Jr. & Todd Dupont

Authors
  1. Jim Douglas Jr.
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  2. Todd Dupont
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This research was supported in part by the National Science Foundation.

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Douglas, J., Dupont, T. Superconvergence for galerkin methods for the two point boundary problem via local projections. Numer. Math. 21, 270–278 (1973). https://doi.org/10.1007/BF01436631

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  • DOI: https://doi.org/10.1007/BF01436631

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