Stabilized finite element method for simulation of freeway traffic

The modeling of traffic flow is a key tool to simulate and predict the behavior of traffic systems. Macroscopic traffic simulation models are based on advection dominated coupled non-linear partial differential equations. The solution of such advection dominated equations with the method of finite elements is leading to the development of stabilization techniques. The choice of suitable stabilization parameters is often application-dependent. A stabilized finite element procedure on the basis of a Galerkin/least-square approximation is presented for systems of transient advection-dominated equations. A general rule for computing suitable element stabilization parameters is outlined which uses the spectral radius of the differential operators and the specific element expansion. The application of this approximation to a macroscopic traffic model shows the applicability of this approach. Simulation results of typical phenomena of jam formation in freeway traffic are presented.