Generalized p-FEM in homogenization

A new finite element method for elliptic problems with locally periodic mic rostructure of length epsilon > 0 is developed and analyzed. It is shown th at the method converges, as epsilon --> 0, to the solution of the homogeniz ed problem with optimal order in epsilon and exponentially in the number of degrees of freedom independent of epsilon > 0. The computational work of t he method is bounded independently of epsilon. Numerical experiments demons trate the feasibility and confirm the theoretical results.