Multiscale finite elements for linear elasticity: Oscillatory boundary conditions

We extend the multiscale finite element method with oscillatory boundary conditions, introduced for scalar elliptic PDEs by Hou and Wu (J. Comput. Phys. 134:169-189, 1997), to the system of anisotropic linear elasticity. We apply the approach for the construction of robust coarse spaces in the context of two-level overlapping domain decomposition preconditioners for multi-phase elastic composites. We explain the construction on a tetrahedral mesh and present numerical results for isotropic materials showing that robustness w.r.t. coefficient variations in the PDE can be achieved even for the class of problems where inclusions of high stiffness cross coarse element boundaries.