Analysis of a linearization scheme for an interior penalty discontinuous Galerkin method for two‐phase flow in porous media with dynamic capillarity effects

Summary We present a linearization scheme for an interior penalty discontinuous Galerkin method for two‐phase porous media flow model, which includes dynamic effects on the capillary pressure. The fluids are assumed immiscible and incompressible, and the solid matrix non‐deformable. The physical laws are approximated in their original form, without using the global or complementary pressures. The linearization scheme does not require any regularization step. Furthermore, in contrast with Newton or Picard methods, there is no computation of derivatives involved. We prove rigourously that the scheme is robust and linearly convergent. We make an extensive parameter study to compare the behaviour of the L‐scheme with the Newton method.