Special finite element methods for a class of second order elliptic problems with rough coefficients
SIAM Journal on Numerical Analysis
A multiscale finite element method for elliptic problems in composite materials and porous media
Journal of Computational Physics
Adaptive hierarchical modeling of heterogeneous structures
Physica D - Special issue originating from the 18th Annual International Conference of the Center for Nonlinear Studies, Los Alamos, NM, May 11&mdash ;15, 1998
Convergence of a Nonconforming Multiscale Finite Element Method
SIAM Journal on Numerical Analysis
A mixed multiscale finite element method for elliptic problems with oscillating coefficients
Mathematics of Computation
Multi-scale finite-volume method for elliptic problems in subsurface flow simulation
Journal of Computational Physics
Finite difference heterogeneous multi-scale method for homogenization problems
Journal of Computational Physics
Nonconforming cell boundary element methods for elliptic problems on triangular mesh
Applied Numerical Mathematics
A Hybrid Discontinuous Galerkin Method for Elliptic Problems
SIAM Journal on Numerical Analysis
Applied Numerical Mathematics
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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 H^1 convergence analysis and numerical examples confirming our analysis are presented.