On approximation of discontinuous solutions to the Buckley–Leverett equation

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.