Two phase flow problem in a porous medium is governed by a system of nonlinear equations. One is an elliptic equation for the pressure and the other is a parabolic equation for the concentration of one of the fluids. Since the pressure appears in the concentration only through its velocity field, we choose a mixed finite element to approximate the pressure equation and use the standard Galerkin...

We present a hybridized discontinuous Petrov–Galerkin (HDPG) method for the numerical solution of steady and time-dependent scalar conservation laws. The method combines a hybridization technique with a local Petrov–Galerkin approach in which the test functions are computed to maximize the inf-sup condition. Since the Petrov–Galerkin approach does not guarantee a conservative solution, we propo...