Flux-splitting schemes for parabolic problems
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 52 (2012) no. 8, pp. 1415-1425
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Splitting with respect to space variables can be used in solving boundary value problems for second-order parabolic equations. Classical alternating direction methods and locally one-dimensional schemes could be examples of this approach. For problems with rapidly varying coefficients, a convenient tool is the use of fluxes (directional derivatives) as independent variables. The original equation is written as a system in which not only the desired solution but also directional derivatives (fluxes) are unknowns. In this paper, locally one-dimensional additional schemes (splitting schemes) for second-order parabolic equations are examined. By writing the original equation in flux variables, certain two-level locally one-dimensional schemes are derived. The unconditional stability of locally one-dimensional flux schemes of the first and second approximation order with respect to time is proved.
@article{ZVMMF_2012_52_8_a4,
author = {P. N. Vabishchevich},
title = {Flux-splitting schemes for parabolic problems},
journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
pages = {1415--1425},
publisher = {mathdoc},
volume = {52},
number = {8},
year = {2012},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZVMMF_2012_52_8_a4/}
}
P. N. Vabishchevich. Flux-splitting schemes for parabolic problems. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 52 (2012) no. 8, pp. 1415-1425. http://geodesic.mathdoc.fr/item/ZVMMF_2012_52_8_a4/