Lecture plan
The topics included are:
- Weak formulation of PDEs
- Finite element methods for elliptic equations
- Finite element spaces
- Building finite element approximations
- Error analysis
- Parabolic PDEs and energy arguments
- A posteriori error estimates and adaptivity
- Iterative solvers and preconditioners
- (Time permitting) Discontinuous Galerkin methods
- (Time permitting) Temporal finite element methods
To be more concise, the curriculum (so far) can be summarised into the following topics.
| Topic | Title | Additional reading |
|---|---|---|
| 0 | Introduction (to the course and finite elements) | Brenner & Scott, Chapter 0 |
| 1 | Weak solutions to PDEs | Quarteroni, Chapter 3.3 |
| 2 | Elliptic finite elements in 1D | Quarteroni, Chapter 4.2-4.3 |
| 3 | Existence and uniqueness | Brenner & Scott, Chapter 2 |
| 4 | Finite element spaces (in 2D) | Brenner & Scott, Chapter 3 |
| 5 | Assembling finite element methods | Quarteroni, Chapter 8 |
| 6 | A posteriori error estimates | Ainsworth & Oden |
| 7 | Parabolic PDEs and energy arguments | Thomée |
| 8 | Mixed finite element methods | Brenner & Scott, Chapter 12 |
| 9 | Discontinuous Galerkin methods | Brenner & Scott, Chapter 15.3 |
| -1 | Recap and exam preparation | Lecture notes |
Note: The lectures are not necessarily based on the "additional reading" resources, and should not be used to replace the lecture notes.
Schedule
Lectures: Wednesday 14:15-16:00 (KJL21) and Thursday 10:15-12:00 (R40).
The lecture content and additional reading will be described as we proceed.
| Lecture | Topics |
|---|---|
| 23.08 | No lecture |
| 24.08 | No lecture |
| 30.08 | 0 |
| 31.08 | 1 |
| 06.09 | 2 |
| 07.09 | 2 & 3 |
| 11.09 | 3 |
| 13.09 | No lecture |
| 14.09 | No lecture |
| 20.09 | 3 & 4 |
| 21.09 | 4 |
| 27.09 | 4 & 5 |
| 28.09 | 5 & 6 |
| 04.10 | 6 & 7 |
| 05.10 | 7 |
| 11.10 | 7 |
| 12.10 | 7 |
| 18.10 | 8 |
| 19.10 | 8 |
| 25.10 | 8 & 9 |
| 26.10 | 9 |
| 01.11 | No lecture |
| 02.11 | Project work |
| 08.11 | No lecture |
| 09.11 | Project work |
| 15.11 | -1 |
| 16.11 | No lecture |
| 22.11 | Project presentations |
| 23.11 | Project presentations |