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Difference Differential Operators with Values at the Midpoints of the Sides of Cells of a Triangular Grid

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Abstract

A grid analog of the formula of integration by parts is constructed and studied for a two-dimensional case in which one of the grid functions is defined at nodes, and the second function is defined at the midpoints of the sides of cells of a simplicial grid in the Cartesian and cylindrical systems of coordinates. Grid analogs of such first-order differential operators as the gradient, divergence, and curl operators, can be naturally defined using this formula.

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Authors and Affiliations

  1. Faculty of Computational Mathematics and Cybernetics, Moscow State University, 119991, Moscow, Russia

    M. N. Sablin

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  1. M. N. Sablin
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Correspondence to M. N. Sablin.

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Translated by N. Berestova

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Sablin, M.N. Difference Differential Operators with Values at the Midpoints of the Sides of Cells of a Triangular Grid. MoscowUniv.Comput.Math.Cybern. 44, 97–108 (2020). https://doi.org/10.3103/S0278641920020065

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  • DOI: https://doi.org/10.3103/S0278641920020065

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