The course presents the mathematical foundation of various numerical methods for the efficient quantification of uncertainty in partial differential equations (PDEs). Mathematical foundations include high dimensional polynomial approximation, sparse grid approximations, generalized polynomial chaos expansions and their summability properties, as well the computer implementation in model problems.
The course will provide a survey of the mathematical properties and the computational realization of the most widely used numerical methods for uncertainy quantification in PDEs from engineering and the sciences. In particular, Monte-Carlo, Quasi-Monte Carlo and their multilevel extensions for PDEs, Sparse grid and Smolyak approximations, stochastic collocation and Galerkin discretizations will be discussed.
| exercise sheet | due by | templates | solutions |
|---|---|---|---|
| sheet 1 | 12 October 2017 | solution 1 | |
| sheet 2 | 26 October 2017 | templates | solution 2, code |
| sheet 3 | 9 November 2017 | solution 3 | |
| sheet 4 | 23 November 2017 | solution 4 | |
| sheet 5 | 7 December 2017 | solution 5 | |
| sheet 6 | 21 December 2017 | solution 6 |
printed lecture notes will be made available
