Geodesic
Alternating triangular schemes for convection-diffusion problems
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 56 (2016) no. 4, pp. 587-604 Cet article a éte moissonné depuis la source Math-Net.Ru

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Explicit-implicit approximations are used to approximate nonstationary convection-diffusion equations in time. In unconditionally stable two-level schemes, diffusion is taken from the upper time level, while convection, from the lower layer. In the case of three time levels, the resulting explicit-implicit schemes are second-order accurate in time. Explicit alternating triangular (asymmetric) schemes are used for parabolic problems with a self-adjoint elliptic operator. These schemes are unconditionally stable, but conditionally convergent. Three-level modifications of alternating triangular schemes with better approximating properties were proposed earlier. In this work, two- and three-level alternating triangular schemes for solving boundary value problems for nonstationary convection-diffusion equations are constructed. Numerical results are presented for a two-dimensional test problem on triangular meshes, such as Delaunay triangulations and Voronoi diagrams. 
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P. N. Vabishchevich; P. E. Zakharov. Alternating triangular schemes for convection-diffusion problems. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 56 (2016) no. 4, pp. 587-604. http://geodesic.mathdoc.fr/item/ZVMMF_2016_56_4_a5/

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