  We consider finite element methods of multiscale type to approximate
solutions for two-dimensional symmetric elliptic partial differential equations
with heterogeneous $L^\infty$ coefficients. The methods are of Galerkin type
and follow the Variational Multiscale and Localized Orthogonal
Decomposition--LOD approaches in the sense that it decouples spaces into
\emph{multiscale} and \emph{fine} subspaces. In a first method, the multiscale
basis functions are obtained by mapping coarse basis functions, based on
corners used on primal iterative substructuring methods, to functions of global
minimal energy. This approach delivers quasi-optimal a priori error energy
approximation with respect to the mesh size, but it is not robust with respect
to high-contrast coefficients. In a second method, edge modes based on local
generalized eigenvalue problems are added to the corner modes. As a result,
optimal a priori error energy estimate is achieved which is mesh and contrast
independent. The methods converge at optimal rate even if the solution has
minimum regularity, belonging only to the Sobolev space $H^1$.
