Location: ETH Zentrum, Machine Laboratory (ML), H Floor, Room ML H41.1

Registration, Opening: Monday, September 9, 8:00 - 8:30

Lectures of I. Babuska (Tuesday, Wednesday):

1. Problems of verification, validation and uncertainties.
2. Problem of specific composite materials used in airplane industry.
3. Problem of solving (deterministic) differential equations with rough coefficients.
4. Homogenization and numerical treatement of the problems discussed in lecture 2. The stochastic formulation.
5. Basics of solving stochastic equations (without white noise) and with uncertainties.

Lectures of M. Chipot (Monday, Tuesday):

1. Nonconvex analysis.
2. Problems generating microstructures.
3. Numerical analysis of microstructures.

Lectures of D. Cioranescu (Monday):

1. Asymptotic Expansion approach to homogenization for elliptic, parabolic, hyperbolic problems.
2. Error estimates, Boundary correctors.
3. Unfolding Approach to homogenization, Two- and Multiple Scales, Error Estimates.

Lectures of W. Hackbusch (Thursday):

1. Iterative schemes and introduction.
2. Two- and multi-grid algorithms, nested iteration.
3. Convergence, smoothing property, approximation property.
4. Nonlinear systems, eigenvalue problems.

Lectures of S. Sauter (Friday):

1. Composite Finite Elements and Multigrid.
2. Multilevel Methods on Complicated Domains.
3. Algebraic Multigrid Methods.

Lectures of C. Schwab (Tuesday, Wednesday, Thursday):

1. Non asymptotic Fourier-Representation of solutions to homogenization problems.
2. Generalized hp-FEM for homogenization problems. Convergence rates.
3. Two-Scale regularity, Two-Scale FEM Error Estimates.
4. Sparse Two-Scale Finite Element Methods.
5. Sparse Finite Element Approximation of Unfolding limiting Problems (see lecture 5 of D. Cioranescu)