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
- Discontinuous Galerkin methods
- Temporal finite element methods
- (Time permitting) Conservative 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 | A posteriori error analysis | Ainsworth & Oden |
| 6 | Non-conforming finite element methods | Brenner & Scott, Chapter 15.3 |
| 7 | Implementation | Quarteroni, Chapter 8 |
| 8 | Parabolic PDEs | Thomée |
| 9 | Finite elements in time | Click here |
Note: The lectures are not necessarily based on the "additional reading" resources, and should not be used to replace the lectures.
Schedule
Lectures: Wednesday 14:15-16:00 (G21) and Thursday 12:15-14:00 (G21).
The lecture content and additional reading will be described as we proceed.
| Lecture | Topics |
|---|---|
| 20.08 | 0 |
| 21.08 | No lecture |
| 27.08 | No lecture |
| 28.08 | No lecture |
| 03.09 | 1 |
| 04.09 | 1 / 2 |
| 10.09 | 2 |
| 11.09 | 2 / 3 |
| 17.09 | 3 |
| 18.09 | 3 |
| 25.09 | 4 |
| 26.09 | 4 |
| 01.10 | 4 / 5 |
| 02.10 | 5 |
| 08.10 | 6 |
| 09.10 | 6 / 7 |
| 15.10 | 7 / 8 |
| 16.10 | 8 |
| 22.10 | 8 |
| 23.10 | 8 |
| 29.10 | 8 |
| 30.10 | 8 / 9 |
| 5.11 | 9 |
| 6.11 | Project |
| 12.11 | Project |
| 13.11 | No lecture |
| 19.11 | 9 |
| 20.11 | Revision |