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Extrapolation in the finite element method with penalty

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Part of the Lecture Notes in Mathematics book series (LNM,volume 430)

Abstract

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.

Keywords

  • Finite Element Method
  • Penalty Method
  • Essential Boundary Condition
  • Satisfy Boundary Condition
  • Optimal Error Estimate

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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© 1974 Springer-Verlag

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King, J.T. (1974). Extrapolation in the finite element method with penalty. In: Colton, D.L., Gilbert, R.P. (eds) Constructive and Computational Methods for Differential and Integral Equations. Lecture Notes in Mathematics, vol 430. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0066273

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  • DOI: https://doi.org/10.1007/BFb0066273

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-07021-4

  • Online ISBN: 978-3-540-37302-5

  • eBook Packages: Springer Book Archive