Mixed Generalized Multiscale Finite Element Method for flow problem in thin domains

In this paper, we construct a class of Mixed Generalized Multiscale Finite Element Methods for the approximation on coarse grid an elliptic problem in thin two-dimensional domains. We consider equation with homogeneous boundary conditions domain walls. For reference solution problem, use Method fine that resolves complex geometry level. To lower dimensional model, Method, which is based some multiscale basis functions velocity fields. The construction local snapshot space takes all possible flows interface between cells into account. order to reduce size and obtain approximation, solve spectral identify dominant modes space. present convergence analysis presented method. Numerical results are problems three testing geometries along errors associated different numbers used field. investigations conducted heterogeneous properties respectively.