Two-Grid Decoupling Method for Elliptic Problems on Disjoint Domains

We propose a two-grid finite element method for solving elliptic problems on disjoint; domains. With this method, the solution of the multi-component domain problem(simple example - two disjoint rectangles) on a fine grid is reduced to the solution of the original problem on a much coarser grid together with solution of several problems (each on a single-component domain) on fine meshes. The advantage is the computational cost although the resulting solution still achieves asymptotically optimal accuracy. Numerical experiments demonstrate the efficiency of the algorithms.