On the solution of incompressible two-phase ow by a p-version discontinuous Galerkin method

where u = − K∇p is the Darcy phase velocity, proportional to the gradient of the phase pressure p . The other coe cients in the model are: the porosity, q a source term, the phase mobility and K the permeability of the porous medium. The di erence between the phase pressures is the capillary pressure pc =pn − pw and we also assume that the sum of the phase saturations is equal to one. The boundary of is divided into three disjoint parts