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
Multi-scale computational homogenization: Trends and challenges
Journal of Computational and Applied Mathematics
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A coupling extended multiscale finite element method is developed for the thermoelastic analysis of heterogeneous multiphase materials. In the method, the weak coupling of thermal and structure is considered and two sets of numerical base functions are constructed for the temperature and displacement fields, respectively. To improve the accuracy of the base functions, the periodic boundary conditions and the oversampling technique are adopted. Numerical results of several representative examples indicate that the proposed method can not only capture the fine scale information in the macroscopic computation but also recover the fine scale solution conveniently.