Abstract
In this paper we modify the usual five-point-difference discretization near the boundary of a general domain as to guarantee the existence of an asymptotic expansion. We generalize and improve results due to Gerschgorin [9], Collatz [8], Mikeladse [11], Wasow [14] and Pereyra-Proskurowski-Widlund [12].
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Böhmer, K. (1979). Asymptotic Expansions for the Discretization Error In Poisson’s Equation on General Domains. In: Schempp, W., Zeller, K. (eds) Multivariate Approximation Theory. ISNM International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série Internationale D’Analyse Numérique, vol 51. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-6289-9_2
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DOI: https://doi.org/10.1007/978-3-0348-6289-9_2
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