Two-scale FEM for homogenization problems

Abstract

The convergence of a two-scale FEM for elliptic problems in divergence form with coefficients and geometries oscillating at length scale ε ≪ 1 is analyzed. Full elliptic regularity independent of e is shown when the solution is viewed as mapping from the slow into the fast scale. Two-scale FE spaces which are able to resolve the e scale of the solution with work independent of ε and without analytical homogenization are introduced. Robust in ε error estimates for the two-scale FE spaces are proved. Numerical experiments confirm the theoretical analysis.