Efficient Multiscale Coarse Approximations for Diffusion Problems in Perforated Domains

The authors propose a low-dimensional coarse approximation space based on a coarse polygonal partitioning of the domain to efficiently solve diffusion problems in perforated domains. The coarse space is spanned by locally discrete harmonic basis functions with piecewise polynomial traces along the subdomain boundaries. The method provides superconvergence for a specific edge refinement procedure, even if the true solution has low regularity.