A multiscale cell boundary element method for elliptic problems

In this paper we introduce the multiscale cell boundary element method (MsCBE method). The method is obtained by applying the oversampling technique of the MsFEM by Hou and Wu T.Y. Hou, X.H. Wu, A multiscale finite element method for elliptic problems in composite materials and porous media, J. Comput. Phys. 134 (1997) 169–189] to the newly developed numerical method, the cell boundary element(CBE) method by the author and his colleagues. The advantage of the MsCBE method is that it preserves flux exactly on arbitrary subdomain without needing the dual mesh. A complete H¹ convergence analysis and numerical examples confirming our analysis are presented.