×

Covariant transformations of basis differential-difference schemes in a plane. (Russian, English) Zbl 1249.65139

Zh. Vychisl. Mat. Mat. Fiz. 51, No. 11, 2033-2041 (2011); translation in Comput. Math. Math. Phys. 51, No. 11, 1915-1922 (2011).
Summary: 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.

MSC:

65L03 Numerical methods for functional-differential equations
34K34 Hybrid systems of functional-differential equations
34K28 Numerical approximation of solutions of functional-differential equations (MSC2010)
65L12 Finite difference and finite volume methods for ordinary differential equations
PDFBibTeX XMLCite
Full Text: DOI