Discontinuous Galerkin approximation of two-phase flows in heterogeneous porous media with discontinuous capillary pressures

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A posteriori error estimates, stopping criteria, and adaptivity for two-phase flows (2013, methodology): “In the context of two-phase flows, the constructions of uα,hτ , α ∈ {n,w}, can be found in [21] for cell-centered finite volume methods, in [14] for vertex-centered finite volume methods, and in [28, 29] for the discontinuous Galerkin method.”
A discontinuous Galerkin method for two-phase flow in a porous medium enforcing H(div) velocityand continuous capillary pressure (2013, unknown): “Similar to [9], the idea is to add a penalty to discontinuity of the capillary pressure.”
Finite volume approximation for an immiscible two-phase flow in porous media with discontinuous capillary pressure (2013, methodology): “A numerical method based on Mixed Finite Element was developed by H. Hoteit and A. Firoozabadi [34], while a Discontinuous Galerkin method has been proposed by A. Ern et al. [24], and its eﬀective implementation was discussed in the contribution of I. Mozolevski and L. Schuh [36].”