Convergence of finite volume schemes for triangular systems of conservation laws

We consider non-strictly hyperbolic systems of conservation laws in triangular form, which turn up in applications like three-phase flows in porous media flow. We device finite volume schemes of Godunov type for these systems that exploit the triangular structure. We prove that the finite volume schemes converge to weak solutions as the discretization parameters tend to zero. Some numerical examples are presented, one of which is related to flows in porous media.