This article gives an example of a study of the convergence of a structural parabolic non-stationary model. In this case, apart from spatial variables, the convergence study must take account, also, by the behavior of the solution over time. We chose for the convergence study, the numerical simulation of a process of diffusion of a fluid into the soil. From a physical point of view, the model is elementary. This mathematical model can be the basis of a more complicated construction (simulators) for complex studies for the distribution and absorption of fluids in the soil of some plantations, especially those arranged for different agricultural crops. The mathematical model used is that of the plane fluid diffusion, into the soil. The results consist of the evolution of the fluid concentration, in the soil, depending of time and of the two spatial variables. The article only exposes the organization of data and the estimation of the convergence of the results. 

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