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Covariant transformations of basis differential-difference schemes in a plane

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Abstract

Consistent difference approximations to differential operators in vector and tensor analysis are constructed in curvilinear coordinates in a plane by applying the basis operator method. They are obtained as a transformation of basis approximations in a Cartesian coordinate system. For the continuum mechanics equations in Lagrangian variables, this approach yields theoretically justified differential-difference schemes whose conservation laws correspond to the continuous case.

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  1. Tomsk State University, pr. Lenina 36, Tomsk, 634050, Russia

    V. A. Korobitsyn

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  1. V. A. Korobitsyn
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Correspondence to V. A. Korobitsyn.

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Original Russian Text © V.A. Korobitsyn, 2011, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2011, Vol. 51, No. 11, pp. 2033–2041.

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Korobitsyn, V.A. Covariant transformations of basis differential-difference schemes in a plane. Comput. Math. and Math. Phys. 51, 1915–1922 (2011). https://doi.org/10.1134/S0965542511110121

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