multiscale finite element method

The advection-diffusion in an inhomogeneous medium with a thin channel is considered.  The multiscale finite element method is applied to solving the formulated model problem.  It is shown that the obtained solution is stable and convergent for sufficiently large Peclet numbers.  Numerical examples are presented and analysed.

The advection-diffusion problem in a thin curvilinear channel is considered. The multiscale finite element method is applied to solving the formulated model problem. It is shown that this method is efficient in the case of sufficiently large Peclet numbers. Numerical examples are presented and analysed.