Mazuriak N. Numerical solving of advection-diffusion problems in an inhomogeneous multiscale medium with a thin channel.

The two-dimensional problem of advection-diffusion-reaction in an inhomogeneous medium with a thin curvilinear channel is considered. A multidimensional mathematical model of the problem is constructed by applying the technique of dimension reducing. The theorems of existence and uniqueness of the solution of the appropriate variational problem are formulated and proved. A theoretical research of the convergence of the multiscale finite element method in its application to advection-diffusion-reaction problems is carried out and the corresponding theoretical estimates are derived. A series of numerical experiments have been performed using the developed software. It is shown that the multiscale finite element method is effective for solving the formulated problem with large Peclet numbers in both homogeneous and multiscale environments.