Convergence of finite volume schemes for triangular systems of conservation laws
Kenneth H. Karlsen, Siddhartha Mishra and Nils Henrik Risebro
Abstract: We consider non-strictly hyperbolic systems of conservation laws in triangular form which arise in applications like three phase flows in porous media. We device simple and efficient finite volume schemes of the Godunov type that exploit the triangular structure. We prove that the finite volume schemes converge to weak solutions as the discretization parameters go to zero. Some numerical examples are presented, one of which is related to flows in porous media.