Lecture plan
The curriculum is taken from A. Quarteroni (Q), Numerical Models for Differential Problems, Third Edition, Springer 2017.
We will also use some material from Brenner & Scott (BS): The Mathematical Theory for Finite Element Methods, Springer 2008.
The topics included are:
- Introduction
- The Poisson equation:
- Weak formulation
- Finite element method
- Implementation
- Error analysis
- Finite element function spaces
- Abstract formalism
- Steady convection-diffusion problem
- Time-dependent convection-diffusion problem.
Schedule
Lectures: Monday 10:15-12:00 (VA2) and Tuesday 10:15-12:00 (R92).
The topics will be described as we proceed.
| Lecture | Topics | Reading | |
|---|---|---|---|
| 22.08 | Introduction. FEM-History and FEM applications. | Slides | |
| 23.08 | Poisson: PDE, Minimization and weak form. | LN-1 and Chapter 1. in Quarteroni | |
| 29.08 | Mathematical Background. | LN-1, Chapter 2. in Quarteroni, and Chapter 1. in Brenner& Scott | |
| 30.08 | Discretization of the Poisson Problem in \(R^1\) : Formulation. | LN-2 and Sections 3.1 and 3.2 in Quarteroni | |
| 31.08 | Discretization of the Poisson Problem in \(R^1\) : Formulation (continue) | LN-2 and Sections 3.1 and 3.2 in Quarteroni | |
| 05.09 | Discretization of the Poisson Problem in \(R^1\): Theory | LN-3 and Sections 4.1-4.3 in Quarteroni | |
| 06.09 | No lecture | ||
| 12.09 | Discretization of the Poisson Problem in \(R^1\): Implementation | LN-3 | |
| 13.09 | FEM for the Poisson Problem in \(R^2\) | LN-4 and Section 4.4 in Quarteroni | |
| 19.09 | FEM for the Poisson Problem in \(R^2\) (continnue) | LN-4 and Section 4.4 in Quarteroni | |
| 20.09 | Abstract FEM: Construction of a Finite Element Space | Chapter 3. in Brenner & Scott | |
| 26.09 | Triangular elements | Chapter 3. in Brenner & Scott | |
| 27.09 | Triangular elements (continued) | Chapter 3. in Brenner & Scott | |
| 03.10 | Quadrilateral Elements | Chapter 3. in Brenner and Scott | |
| 04.10 | Isoparametric mapping | Deformed Geometries, IFEM Ch16 and IFEM Ch17 | |
| 10.10 | Adaptive FEM (AFEM): A priori estimates | AFEM-notes_TMA4220. (See Blackboard) | |
| 11.10 | Adaptive FEM (AFEM): A posteriori estimates | AFEM-notes_TMA4220. (See Blackboard) | |
| 17.10 | No lecture | ||
| 18.10 | No lecture | ||
| 24.10 | No lecture | ||
| 25.10 | Adaptive FEM (AFEM): Adaptive refinement | AFEM-notes_TMA4220. (See Blackboard) | |
| 26.10 | Spectrum of Laplace operator | Spectrum of Laplace Operator | |
| 31.10 | Time-dependent diffusion | Time-dependent diffusion | |
| 01.11 | Convection-Diffusion. Introduction | ER-1 | |
| 02.11 | Convection-Diffusion: Example and Theory | ER-2, ER-3 | |
| 07.11 | No lecture | ||
| 08.11 | No lecture | ||
| 14.11 | No lecture | ||
| 15.11 | No lecture | ||
| 21.11 | No lecture | ||
| 22.11 | No lecture |