Streamline diffusion method for treating coupling equations of hyperbolic scalar conservation laws

In this paper we study the streamline diffusion finite element method for treating the one-dimensional time dependent coupling equations of two hyperbolic conservation laws. We derive optimal convergence rates, showing an a priori error estimate of order O ( h k + 1 / 2 ) in domains where the exact solution is smooth; here h is the mesh width and k is the degree of the piecewise polynomial functions spanning the finite element subspace. The corresponding optimal convergence rate for the standard Galerkin method is of order O ( h k ) . We justify this advantage of the streamline diffusion method versus the standard Galerkin with a series of numerical examples.