Hybrid Localized Spectral Decomposition for Multiscale Problems

We consider a finite element method for elliptic equations with heterogeneous and possibly high-contrast coefficients based on primal hybrid formulation. assume minimal regularity of the solutions. A space decomposition as in FETI BDCC induces an embarrassingly parallel preprocessing leads to final system size independent coefficients. The resulting solution is equilibrium, all PDEs involved are elliptic. One problems pre-processing step nonlocal but exponentially decaying solutions, enabling practical scheme where basis functions have extended, still local, support. To make robust respect coefficients, we enrich via local eigenvalue problems, obtaining optimal priori error estimate that mitigates effect having different magnitudes. technique developed dimensional easy extend other such elasticity.