News
29/8: The schedule is fixed and an email was sent to all participants. Please choose a topic that you want to present by 31/8.22/8: The first meeting is scheduled for Tuesday, August 29, 10:00 in MVL:14
Teacher
Course coordinator: Annika LangEmail: annika.lang@chalmers.se
Office: MVL2086
Course description
Random partial differential equations (RPDE) are partial differential equations where someof the parameters suffer under uncertainty. The uncertainty can be due to the lack of know-
ledge, measurement errors, or the complexity of exact deterministic model. Possible uncertain
parameters can influence the right hand side of the equation, the operator, the boundary, or
the initial condition. The goal of this course is to discuss existence and uniqueness of solutions
to RPDE and to derive efficient approximation methods to estimate solutions which includes
the numerical analysis of the convergence behavior of the considered schemes.
The course will start in the end of August and run twice a week (4 hours) until the end of
October (LP1 2017/18). The schedule will be decided by the participants at an introductory
meeting.
Course literature
will be updated continuously and still depends on the interest of the audience- Lecture notes (LN) distributed to the participants
- and references therein
Schedule
| Tuesday 29/8 10-12 MVL:14 |
Introduction Discussion of the schedule (Annika) |
| Tuesday 5/9 13-15 MVL:14 |
Preliminaries in Functional
Analysis and Probability Theory (Annika) |
| Thursday 7/9 13-15 MVL:14 |
Introduction to elliptic PDE and
equations with stochastic rhs (LN 3.1, 3.2(.0)) (Annika) |
| Tuesday 12/9 13-15 MVL:14 |
Galerkin approximation of
moments (LN 3.2.1) (Fardin) |
| Thursday 14/9 13-15 MVL:14 |
Galerkin approximation of moments
(LN 3.2.1) (Fardin) |
| Tuesday 19/9 13-15 MVL:14 |
Sparse tensor approximations (LN
3.2.2) (Alice) |
| Thursday 21/9 13-15 MVL:14 |
Sparse tensor approximations (LN
3.2.2) (Alice) |
| Tuesday 26/9 13-15 MVL:14 |
Introduction to elliptic PDE with stochastic operator and
finite element approximation (LN 3.3, 3.3.1,3.3.1.1) (Per) |
| Thursday 28/9 13-15 MVL:14 |
Introduction to elliptic PDE with stochastic operator and
finite element approximation (LN 3.3, 3.3.1,3.3.1.1) (Per) |
| Tuesday 3/10 13-15 MVL:15 |
Introduction to multilevel Monte Carlo and approximation of
moments (LN 3.3.1.2) (Anders) |
| Tuesday 10/10 13-15 MVL:15 |
Polynomial chaos expansions (LN 3.3.2.1) (Helga) |
| Thursday 12/10 13-15 MVL:14 |
Polynomial chaos expansions (LN 3.3.2.1) (Helga) |
| Tuesday 17/10 13-15 MVL:15 |
Equivalent formulation/transformation (LN 3.3.2.2) (Milo) |
| Friday 20/10 13-15 MVL:15 |
Approximation of Legendre chaos expansions (LN 3.3.2.3) (Milo) |
| Thursday 26/10 13-15 MVL:14 |
Project presentations |