Geodesic
Difference schemes on nonuniform grids for the two-dimensional convection-diffusion equation
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 57 (2017) no. 12, pp. 2042-2052 Cet article a éte moissonné depuis la source Math-Net.Ru

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New second-order accurate monotone difference schemes on nonuniform spatial grids for two-dimensional stationary and nonstationary convection-diffusion equations are proposed. The monotonicity and stability of the solutions of the computational methods with respect to the boundary conditions, the initial condition, and the right-hand side are proved. Two-sided and corresponding a priori estimates are obtained in the grid norm of $C$. The convergence of the proposed algorithms to the solution of the original differential problem with the second order is proved. 
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P. P. Matus; Le Minh Hieu. Difference schemes on nonuniform grids for the two-dimensional convection-diffusion equation. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 57 (2017) no. 12, pp. 2042-2052. http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_12_a6/

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