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Numerische Mathematik

, Volume 23, Issue 2, pp 153–165 | Cite as

New error bounds for the penalty method and extrapolation

  • J. T. King
Article

Abstract

New error bounds are obtained for the Babuška penalty method which justify the use of extrapolation. For the problemΔu=f in Ω,u=g on ∂Ω we show that, for a particular choice of boundary weight, repeated extrapolation yields a quasioptimal approximate solution. For example, the error in the second extrapolate (using cubic spline approximants) isO (h3) when measured in the energy norm. Nearly optimalL2 error estimates are also obtained.

Keywords

Error Estimate Approximate Solution Mathematical Method Error Bound Energy Norm 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 1974

Authors and Affiliations

  • J. T. King
    • 1
  1. 1.Department of Mathematical SciencesUniversity of CincinnatiCincinnatiUSA

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