Estimation Problem of Advection-Diffusion Analysis Using Kalman Filter

This paper presents Advection-Diffusion Analysis Using Kalman Filter FEM. The Advection-Diffusion phenomenon often can be seen close to one. The Diffusion phenomenon is, for example, seepage flow problem, heat transfer problem, atmosphere diffusion and so on. On the other hands, the Advection-Diffusion phenomenon is, for example, ground water problem, water pollution, soil pollution. In particular, pollution phenomenon is employed for the Advection-Diffusion equation. In this equation, the Galerkin method is applied to discretization in space. The forward difference method is employed for discretization in time. The Kalman Filter is applied to frequently for the solution of time series analysis including the observation and the system noise. The Kalman Filter finite element method is the combination method of the Kalman Filter and FEM, and is capable of estimating in time and space directions