Localised filtering for transport models

Interface control is an important area in applications of Domain Decomposition (DD) for linear advection-diffusion equations, since it attempts to minimize the errors committed by DD methods. In this work a localised control and estimation strategy, confined to selected sub-domains, that combines DD and filtering is proposed for linear non-stationary advection-diffusion equations. This approach mitigates the error introduced by DD and Finite Element Method (FEM) discretization and, in addition, it allows to combine observations (for instance, sensor´s readings) with numerical solutions of advection-diffusion equations. The latter is of utmost importance for data assimilation methods widely applied in geophysics.