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(hk+1/2)O(hk+1/2) in domains where the exact solution is smooth; here hh is the mesh width and kk 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(hk)O(hk). We justify this advantage of the streamline diffusion method versus the standard Galerkin with a series of numerical examples.