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Improved difference schemes for the Dirichlet problem of Poisson's equation in the neighbourhood of corners

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Summary

The standard 5-point difference scheme for the model problem Δu=f on a special polygonal domain with given boundary values is modified at a few points in the neighbourhood of the corners in such a way that the order of convergence at interior points is the same as in the case of a smooth boundary. As a side result improved error bounds for the usual method in the neighbourhood of corners are given.

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Authors and Affiliations

  1. Leibniz-Rechenzentrum der Bayerischen Akademie der Wissenschaften, Barerstr. 21, D-8000, München 2, Germany (Fed. Rep.)

    C. Zenger & H. Gietl

Authors
  1. C. Zenger
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  2. H. Gietl
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Zenger, C., Gietl, H. Improved difference schemes for the Dirichlet problem of Poisson's equation in the neighbourhood of corners. Numer. Math. 30, 315–332 (1978). https://doi.org/10.1007/BF01411846

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  • DOI: https://doi.org/10.1007/BF01411846

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