Numerische Mathematik

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

New error bounds for the penalty method and extrapolation

  • J. T. King


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.


Error Estimate Approximate Solution Mathematical Method Error Bound Energy Norm 
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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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