Solution of the traffic flow equation using the finite element method

Abstract

In this document we will study and solve the nonlinear partial differential equation, with initial conditions for vehicle entry that serves to model the dynamics of traffic flow. To find a numerical solution to the dynamics that govern the behavior of traffic flow, the Finite Element Method in a spatial dimension was used. In accordance with the temporal dynamics, simulations were developed to know the flow in terms of time. The numerical solution is interesting for predicting the number of vehicles at the entrance to a high-flow road. Some theorems are enunciated that guarantee the existence of the solution and the uniqueness is given by the boundary conditions.