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Homogenisation of periodic structures
- Asymptotic homogenization theory for elliptic problems
- Boundary correctors
- Error estimates
- Homogenisation of parabolic and hyperbolic problems
Variational methods for problems with microstructures
- Nonconvex analysis
- Problems generating microstructures
- Numerical analysis of microstructures
Generalised FEM for multiscale problems
- Fourier analysis of homogenisation problems
- Two and multiscale regularity
- Analysis and implementation of multiscale FEM
Real life problems: modelling and numerics
- Problem of verification, validation and uncertainties
- Problem of specific composite materials used in airplane industry
- Solving (deterministic) differential equations with rough coefficients
- Homogenization and numerical treatment of the problems above.
The stochastic formulation.
- Basics of solving stochastic equations (without noise) and with
uncertainties
Multigrid solvers for elliptic problems
on complicated domains
- Introduction to multigrid methods
- Composite finite elements
- Multiscale discretisation
- Implementation
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