# LMS-EPSRC Short Course on Multiscale Methods

## Monday 16 – Friday 20 April 2007

## Timetable

(all days have the same format)

Lecture Notes by **G Pavliotis and A Stuart**

**Sunday 15 April 2007**

4:00–6:00 Tea & Welcome - Mathematics Institute Common Room, Zeeman Building

6:00–7:00 Dinner - Mathematics Institute Common Room, Zeeman Building

**Monday 16 April 2007**

9:30–10:45 **A Stuart** (Warwick) *Averaging and homogenization for finite dimensional systems of linear equations*

10:45–11:30 Coffee/Tea in Mathematics Institute Common Room

11:30–12:45 **G Pavliotis** (Imperial) *PDEs – Elliptic PDEs. Formal calculations and examples
*12:45–2:15 Lunch in Mathematics Institute Common Room

2:15–3:15 Guest speaker:

**J Willis**(Cambridge)

*Elastodynamics of composites*

3:15–4:00 Coffee/Tea in Mathematics Institute Common Room

4:00–5:30

*Tutorial Session*

5:30 for 6:00 Dinner in Mathematics Institute Common Room<

**Tuesday 17 April 2007**

9:30–10:45 **A Stuart** (Warwick) *Stochastic Processes: Introduction to SDEs (Ito formula, Kolmogorov and Fokker-Planck equations; ergodicity)*

10:45–11:30 Coffee/Tea in Mathematics Institute Common Room

11:30–12:45 **G Pavliotis** (Imperial) *PDEs – Parabolic PDEs. Formal calculations and examples*

12:45–2:15 Lunch in Mathematics Institute Common Room

2:15–3:15 Guest speaker: **B Engquist** (Austin) *Heterogeneous multi-scale methods*

3:15–4:00 Coffee/Tea in Mathematics Institute Common Room

4:00–5:30 *Tutorial Session*

6:00 Dinner at Xanana in the Students' Union Building, University of Warwick

**Wednesday 18 April 2007**

9:30–10:45 **A Stuart** (Warwick) *Stochastic Processes: Averaging. Formal calculations and examples*

10:45–11:30 Coffee/Tea in Mathematics Institute Common Room

11:30–12:45 **G Pavliotis** (Imperial) *PDEs – Transport. Formal calculations and examples*

12:45–2:15 Lunch at EAT restaurant in the University of Warwick Arts Centre

2:15–3:15 Guest speaker: **A Abdulle **(Edinburgh)* Numerical methods based on a macro-to-micro approach for multiscale PDEs*

3:15–4:00 Coffee/Tea in Mathematics Institute Common Room

4:00–5:30 *Tutorial Session
*5:30 for 6:00 Dinner in Mathematics Institute Common Room

**Thursday 19 April 2007**

9:30–10:45 **A Stuart** (Warwick) *Stochastic Processes: Homogenization. Formal calculations and examples*

10:45–11:30 Coffee/Tea in Mathematics Institute Common Room

11:30–12:45 **G Pavliotis** (Imperial) *PDEs – Properties of the homogenized coefficients*

12:45–2:15 Lunch in Mathematics Institute Common Room

2:15–3:15 Guest speaker: **G Friesecke** (Munich/Warwick) *Quantum mechanical modelling of molecules: multiscale aspects*

3:15–4:00 Coffee/Tea in Mathematics Institute Common Room

4:00–5:30 *Tutorial Session
*5:30 for 6:00 Dinner in Mathematics Institute Common Room

**Friday 20 April 2007**

9:30–10:45 **A Stuart** (Warwick) *Stochastic Processes: Theory – use of Poisson equations, weak and strong convergence*

10:45–11:30 Coffee/Tea in Mathematics Institute Common Room

11:30–12:45 **G Pavliotis** (Imperial) *PDEs – Theory – two-scale convergence; maximum principle*

12:45–2:15 Lunch in Mathematics Institute Common Room

2:15–3:15 Guest speaker: **Y Efendiev** (Texas A&M) *Multiscale finite element methods using limited global information*

3:15–4:00 Coffee/Tea in Mathematics Institute Common Room

4:00–5:30 *Tutorial Session
*6:00 Wine, juices and snacks in Mathematics Institute Common Room

**How to get to
Warwick University**

**Contact:**

Mathematics Research Centre

Zeeman Building

University of Warwick

Coventry CV4 7AL - UK

**E-mail:**

mrc@maths.warwick.ac.uk