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Superconvergence analysis of approximate boundary-flux calculations

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Summary

Certain projection post-processing techniques have been proposed for computing the boundary flux for two-dimensional problems (e.g., see Carey, et al. [5]). In a series of numerical experiments on elliptic problems they observed that these post-processing formulas for approximate fluxes were almost (O(h 2)-accurate for linear triangular elements. In this paper we prove that the computed boundary flux isO(h 2 ln 1/h)-accurate in the maximum norm for the partial method of [5]. If the solutionuφH 3(Ω) then the boundary flux error isO(h 3/2) in theL 2-norm.

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Authors and Affiliations

  1. Texas Institute for Computational Mechanics, The University of Texas at Austin, 78712-1085, Austin, TX, USA

    A. I. Pehlivanov & G. F. Carey

  2. University of Wyoming, 82071, Laramie, WY, USA

    R. D. Lazarov & S. S. Chow

Authors
  1. A. I. Pehlivanov
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  2. R. D. Lazarov
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  3. G. F. Carey
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  4. S. S. Chow
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Pehlivanov, A.I., Lazarov, R.D., Carey, G.F. et al. Superconvergence analysis of approximate boundary-flux calculations. Numer. Math. 63, 483–501 (1992). https://doi.org/10.1007/BF01385871

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