Fixed-Point and STILS Method to Solve a Coupled System of Transport Equations

Abstract

In this paper, a coupled system of two transport equations is studied. The techniques are a fixed-point and Space-Time Integrated Least Square (STILS) method. The nonstationary advective transport equation is transformed to a “stationary” one by integrating space and time. Using a variational formulation and an adequate Poincare inequality, we prove the existence and the uniqueness of the solution. The transport equation with a nonlinear feedback is solved using a fixed-point method.