FEM-MsFEM for an interface-coupled parabolic problem

In this paper, we propose and analyze a finite element coupled multiscale finite element method (FEM-MsFEM) for an interface-coupled parabolic problem. The problem involves a coefficient with multiscale characteristics in one region and in the other region without such feature. Our algorithm consists of two main steps: first, solving for the multiscale basis functions in the multiscale region via parallel computation; and second, decoupling the interface-coupled parabolic problem using a data-passing partitioned scheme. This approach allows for the problem to be solved on relatively coarse grids, thereby reducing computational costs. Under suitable assumptions for the multiscale coefficient, we establish the unconditional stability and provide error estimates for the algorithm. The effectiveness of our method is demonstrated through several numerical experiments.