We consider the 2-dimensional anisotropic advection-reaction equation posed on the square S=[-1,1]x[-1,1] described by u_t+u·u_x+e·u_yy=f on [0,T]xS and u_n=0 on the boundary of S. We solve this equation by using a standard finite element method implemented in FreeFem++. For the approximation of the term u_t+u·u_x we use the Characteristics-Galerkin Method suggested in the documentation of Freefem++

The video corresponds to the simulation with e=0.1.