Geodesic
A numerical method for solving diffusion-type equations based on a multigrid method
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 50 (2010) no. 8, pp. 1438-1461

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A new numerical algorithm based on multigrid methods is proposed for solving equations of the parabolic type. Theoretical error estimates are obtained for the algorithm as applied to a two-dimensional initial-boundary value model problem for the heat equation. The good accuracy of the algorithm is demonstrated using model problems including ones with discontinuous coefficients. As applied to initial-boundary value problems for diffusion equations, the algorithm yields considerable savings in computational work compared to implicit schemes on fine grids or explicit schemes with a small time step on fine grids. A parallelization scheme is given for the algorithm. 
@article{ZVMMF_2010_50_8_a7,
     author = {M. E. Ladonkina and O. Yu. Milyukova and V. F. Tishkin},
     title = {A numerical method for solving diffusion-type equations based on a multigrid method},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1438--1461},
     publisher = {mathdoc},
     volume = {50},
     number = {8},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2010_50_8_a7/}
}
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M. E. Ladonkina; O. Yu. Milyukova; V. F. Tishkin. A numerical method for solving diffusion-type equations based on a multigrid method. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 50 (2010) no. 8, pp. 1438-1461. http://geodesic.mathdoc.fr/item/ZVMMF_2010_50_8_a7/