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.