  We propose a multiscale approach for an elliptic multiscale setting with
general unstructured diffusion coefficients that is able to achieve high-order
convergence rates with respect to the mesh parameter and the polynomial degree.
The method allows for suitable localization and does not rely on additional
regularity assumptions on the domain, the diffusion coefficient, or the exact
(weak) solution as typically required for high-order approaches. Rigorous a
priori error estimates are presented with respect to the involved
discretization parameters, and the interplay between these parameters as well
as the performance of the method are studied numerically.
