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BIT Numerical Mathematics

, Volume 54, Issue 4, pp 873–900 | Cite as

Error estimation based on locally weighted defect for boundary value problems in second order ordinary differential equations

  • Winfried Auzinger
  • Othmar Koch
  • Amir Saboor Bagherzadeh
Article

Abstract

We investigate efficient asymptotically correct a posteriori error estimates for the numerical approximation of two-point boundary value problems for second order ordinary differential equations by piecewise polynomial collocation methods. Our error indicators are based on the defect of the collocation solution with respect to an associated exact difference scheme and backsolving using a cheap, low order finite-difference scheme. We prove high asymptotical correctness of this error indicator and illustrate the theoretical analysis by numerical examples.

Keywords

Second order boundary value problems Collocation methods Asymptotically correct a posteriori error estimates  Defect correction principle Exact difference scheme Supraconvergence 

Mathematics Subject Classification (2000)

65L10 65L60 

Notes

Acknowledgments

We would like to thank Mechthild Thalhammer for helpful comments, and Gerhard Kitzler for realizing numerical experiments in Matlab.

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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  • Winfried Auzinger
    • 1
  • Othmar Koch
    • 1
  • Amir Saboor Bagherzadeh
    • 2
  1. 1.Institute for Analysis and Scientific ComputingVienna University of TechnologyViennaAustria
  2. 2.Institute of Structural MechanicsBauhaus UniversityWeimarGermany

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