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

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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. 
@article{ZVMMF_2017_57_12_a6,
     author = {P. P. Matus and Le Minh Hieu},
     title = {Difference schemes on nonuniform grids for the two-dimensional convection-diffusion equation},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {2042--2052},
     publisher = {mathdoc},
     volume = {57},
     number = {12},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_12_a6/}
}
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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/