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Some topological and geometrical problems arising in projective-difference methods for the triangulation of a domain

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Abstract

In this paper the problem of the partition of a polygon Ω into quadrilaterals (quadrangles and triangles) is studied, for which four given boundary pointsA i (1⩽i⩽4) become the vertices of a quadrilateral, and the partition itself is topologically equivalent to a special partition of a rectangle Q into rectangles with sides parallel to the sides of Q. This problem is closely connected with the problem of choosing a basis of piecewise linear functions in the projective-difference method, for which the projective-difference analog of the operator -Δ ≡-(∂2/∂x2 + ∂2/∂y2) for a boundary-value problem in Ω turns out to be spectrally equivalent to its simplest difference analog in a rectangle (see [1–5]).

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Literature cited

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Authors and Affiliations

  1. M. V. Lomonosov Moscow State University, USSR

    E. G. D'yakonov

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  1. E. G. D'yakonov
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Translated from Matematicheskii Zametki, Vol. 21, No. 3, pp. 427–442, March, 1977.

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D'yakonov, E.G. Some topological and geometrical problems arising in projective-difference methods for the triangulation of a domain. Mathematical Notes of the Academy of Sciences of the USSR 21, 238–245 (1977). https://doi.org/10.1007/BF01106751

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  • DOI: https://doi.org/10.1007/BF01106751

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