Domain Decomposition for a linear advection-diffusion equation by means of minimax filtering

In this work a novel strategy that combines Domain Decomposition, Differential Algebraic Equations (DAE) and Minimax Estimation is created to contruct a numerical solution for a linear non stationary advection-diffusion equation. The proposed approach helps to control the error introduced by Domain Decomposition and FEM discretisation and allows to combine observations with solutions of the advection-diffusion equation.