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The paper addresses a numerical method for solving second order elliptic partial differential equations that describe fields inside heterogeneous media. The scope is general and treats the case of rough coefficients, i.e., coefficients with values in . This class of coefficients includes as examples media with microstructure as well as media with multiple nonseparated length scales. The approach taken here is based on the the generalized finite element method (GFEM) introduced in [I. Babuska, G. Caloz, and J. E. Osborn, SIAM J. Numer. Anal., 31 (1994), pp. 945–981] and elaborated in [I. Babuska, U. Banerjee, and J. Osborn, Int. J. Comput. Methods, 1 (2004), pp. 67–103], [I. Babuska and J. Melenk, Internat. J. Numer. Methods Engrg., 40 (1997), pp. 727–758], and [T. Strouboulis, I. Babuska, and K. Copps, Comput. Methods Appl. Mech. Engrg., 181 (2001), pp. 43–69]. The GFEM is constructed by partitioning the computational domain into a …