Two-scale FEM for homogenization problems

Two-Scale FEM for Homogenization Problems

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 ana...

Sparse Two-Scale FEM for Homogenization Problems

We analyze two-scale Finite Element Methods for the numerical solution of elliptic homogenization problems with coefficients oscillating at a small length scale ε 1. Based on a refined two-scale regularity on the solutions, two-scale tensor product FE spaces are introduced and error estimates which are robust (i.e. independent of ε) are given. We show that under additional two-scale regularity ...

Homogenization via p-FEM for Problems

Homogenization and Two - Scale Convergence *

Following an idea of G. Nguetseng, the author defines a notion of "two-scale" convergence, which is aimed at a better description of sequences of oscillating functions. Bounded sequences in L2(f) are proven to be relatively compact with respect to this new type of convergence. A corrector-type theorem (i.e., which permits, in some cases, replacing a sequence by its "two-scale" limit, up to a st...

Generalized p-FEM in homogenization

A new nite element method for elliptic problems with locally periodic microstructure of length " > 0 is developed and analyzed. It is shown that the method converges, as " ! 0, to the solution of the homogenized problem with optimal order in " and exponentially in the number of degrees of freedom independent of " > 0. The computational work of the method is bounded independently of ". Numerical...