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.
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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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