Geodesic
Numerical algorithm for solving diffusion equations on the basis of multigrid methods
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 49 (2009) no. 3, pp. 518-541

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A new effective algorithm based on multigrid methods is proposed for solving parabolic equations. The algorithm preserves implicit-scheme advantages (such as stability, accuracy, and conservativeness) while it involves a considerably reduced amount of arithmetic operations at every time level. The absolute stability, conservativeness, and convergence of the algorithm is proved theoretically using one- and two-dimensional initial-boundary value model problems for the heat equation. The error of the solution is estimated. The good accuracy of the method is demonstrated using two-dimensional model problems, including ones with discontinuous coefficients. 
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     title = {Numerical algorithm for solving diffusion equations on the basis of multigrid methods},
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M. E. Ladonkina; O. Yu. Milyukova; V. F. Tishkin. Numerical algorithm for solving diffusion equations on the basis of multigrid methods. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 49 (2009) no. 3, pp. 518-541. http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_3_a11/