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New a posteriori error estimates for singular boundary value problems

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Abstract

In this paper, we discuss the asymptotic properties and efficiency of several a posteriori estimates for the global error of collocation methods. Proofs of the asymptotic correctness are given for regular problems and for problems with a singularity of the first kind. We were also strongly interested in finding out which of our error estimates can be applied for the efficient solution of boundary value problems in ordinary differential equations with an essential singularity. Particularly, we compare estimates based on the defect correction principle with a strategy based on mesh halving.

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Authors and Affiliations

  1. Vienna University of Technology, Vienna, Austria

    Winfried Auzinger, Othmar Koch, Dirk Praetorius & Ewa Weinmüller

Authors
  1. Winfried Auzinger
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  2. Othmar Koch
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  3. Dirk Praetorius
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  4. Ewa Weinmüller
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Corresponding author

Correspondence to Winfried Auzinger.

Additional information

Communicated by C. Brezinski

AMS subject classification

65L05

Supported in part by the Austrian Research Fund (FWF) grant P-15072-MAT and SFB Aurora.

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Auzinger, W., Koch, O., Praetorius, D. et al. New a posteriori error estimates for singular boundary value problems. Numer Algor 40, 79–100 (2005). https://doi.org/10.1007/s11075-005-3791-5

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  • DOI: https://doi.org/10.1007/s11075-005-3791-5

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