Mixed Variational Formulation and Mixed-Hybrid Discretization of the Transport Equation

We introduce a new variational formulation of the transport equation based on a mixed form of the transport equation. We prove some theoretical results about existence and uniqueness of the solution of this abstract problem by using desirable functional spaces. We then apply a mixed and hybrid finite element method to discretize the transport equation by introducing appropriate basis functions. We present some numerical results to illustrate the efficiency of our method.