Geodesic
Covariant transformations of basis differential-difference schemes in a plane
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 51 (2011) no. 11, pp. 2033-2041 
V. A. Korobitsyn. Covariant transformations of basis differential-difference schemes in a plane. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 51 (2011) no. 11, pp. 2033-2041. http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_11_a6/
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Voir la notice de l'article provenant de la source Math-Net.Ru

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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