Two-scale FEM for homogenization problems
Seminar for Applied Mathematics, ETH-Zentrum,
CH-8092 Zürich, Switzerland. email@example.com.
Revised: 8 April 2002
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 ε 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 ε 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.
Mathematics Subject Classification: 65N30
Key words: Homogenization / two-scale regularity / Finite Element Method (FEM) / two-scale FEM.
© EDP Sciences, SMAI, 2002