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 (h 3) when measured in the energy norm. Nearly optimalL 2 error estimates are also obtained.
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King, J.T. New error bounds for the penalty method and extrapolation. Numer. Math. 23, 153–165 (1974). https://doi.org/10.1007/BF01459948
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DOI: https://doi.org/10.1007/BF01459948