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Consistent grid analogs of invariant differential and boundary operators on an irregular triangular grid in the case of a grid nodal approximation

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Abstract

Grid analogs of invariant first-order differential operators and boundary operators are constructed on an irregular triangular grid. They are consistent in the sense of satisfying the grid analogs of integral relations that are consequences of the Gauss-Ostrogradskii formula for the divergence of a vector field as the product of a scalar and a vector, the vector product of vectors, or the inner product of a vector and a dyad. Construction is done using a grid-operator interpretation of integral relations written for piecewise linear interpolations of grid functions defined at the grid nodes. It is shown how to use consistent grid operators in constructing correct grid approximations of inhomogeneous boundary value problems at the operator level.

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Authors and Affiliations

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

    M. N. Sablin, N. V. Ardelyan & K. V. Kosmachevskii

Authors
  1. M. N. Sablin
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  2. N. V. Ardelyan
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  3. K. V. Kosmachevskii
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Correspondence to M. N. Sablin.

Additional information

Original Russian Text © M.N. Sablin, N.V. Ardelyan, K.V. Kosmachevskii, 2015, published in Vestnik Moskovskogo Universiteta. Vychislitel’naya Matematika i Kibernetika, 2015, No. 2, pp. 3–10.

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Sablin, M.N., Ardelyan, N.V. & Kosmachevskii, K.V. Consistent grid analogs of invariant differential and boundary operators on an irregular triangular grid in the case of a grid nodal approximation. MoscowUniv.Comput.Math.Cybern. 39, 49–57 (2015). https://doi.org/10.3103/S0278641915020077

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  • DOI: https://doi.org/10.3103/S0278641915020077

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