Extrapolation in the finite element method with penalty

  • J. Thomas King
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 430)


Consider the model problem Δu=f in Ω, u=0 on δΩ. Here Ω is a bounded open subset of Rn with smooth boundary, δΩ. The penalty method provides a method for obtaining an approximate solution without requiring the approximant to satisfy boundary conditions. Unfortunately, we pay a price for this convenience, namely loss of accuracy. We show that this difficulty may be alleviated by a particular type of extrapolation process. For a particular choice of boundary weight in the penalty method we show that repeated extrapolation always yields "optimal" error estimates in the energy norm.


Finite Element Method Penalty Method Essential Boundary Condition Satisfy Boundary Condition Optimal Error Estimate 
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Copyright information

© Springer-Verlag 1974

Authors and Affiliations

  • J. Thomas King
    • 1
  1. 1.Department of Mathematical SciencesUniversity of CincinnatiCincinnati

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