Corrigendum to “Discontinuous Galerkin approximation of two-phase flows in heterogeneous porous media with discontinuous capillary pressures” [Comput. Methods Appl. Mech. Engrg. 199 (2010) 1491–1501]

The results presented in Fig. 5 of the published paper need to be corrected. The focus of that paper was the downstream (relative to convection) propagation of the saturation front and its interaction with the interface separating the two rocks with distinct capillary pressure curves. These phenomena are correctly handled by the proposed numerical scheme. However, for the chosen physical parameters and the selected observation times in Fig. 5, there should also be some upstream propagation of the saturation front due to degenerate diffusion. The reason for having missed this effect comes from the discretization of the saturation equation, which is a (nonlinear) convection–diffusion equation with degenerate diffusion and rough initial data (piecewise constant). Using weighted averages and harmonic penalties in the discontinuous Galerkin (dG) method will not propagate the left saturation front upstream. Instead, the usual dG method with arithmetic averages and penalties will propagate this front. However, the weighted dGmethod performs better than the arithmetic dGmethod, at least on moderately refined meshes, to capture the downstream propagation of the right saturation front and its interaction with the rock interface. On highly refined meshes, the performances of the two