Geodesic
On approximation of discontinuous solutions to the Buckley--Leverett equation
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 15 (2012) no. 3, pp. 271-280

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In this paper, the Lax–Wendroff and “cabaret” schemes for the Buckley–Leverett equation are studied. It is shown that these schemes represent unstable solutions. The choice of an unstable solution depends on the Courant number, only. The finite element version of the “cabaret” scheme is given equation are studied. It is shown that these schemes represent unstable solutions. The choice of an unstable solution depends on the Courant number, only. The finite element version of the “cabaret” scheme is given. 
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     author = {Yu. M. Laevsky and T. A. Kandryukova},
     title = {On approximation of discontinuous solutions to the {Buckley--Leverett} equation},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
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Yu. M. Laevsky; T. A. Kandryukova. On approximation of discontinuous solutions to the Buckley--Leverett equation. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 15 (2012) no. 3, pp. 271-280. http://geodesic.mathdoc.fr/item/SJVM_2012_15_3_a3/