Lecture plan
The curriculum is taken from A. Quarteroni (Q), Numerical Models for Differential Problems, Springer 2008.
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: Tuesday and Wednesday.
Known changes are listed.
The topics will be described as we proceed.
| Lecture | Topics | Reading |
|---|---|---|
| 20.08 | Introduction. FEM-History and FEM applications. | |
| 21.08 | Poisson: PDE, Minimization and weak form. | LN-1 and Chapter 1. in Quarteroni |
| 27.08 | Mathematical Background. | Chapter 2. in Quarteroni |
| 28.08 | Definitions of Lebesgue and Sobolov spaces | Chapter 1. in Brenner & Scott |
| 03.09 | Abstract variational formulation of Poisson | LN-1 |
| 04.09 | Discretization of the Poisson Problem in \(R^1\) : Formulation. | LN-2 |
| 10.09 | Discretization of the Poisson problem in \(R^1\). Formulation (continue) | LN-2 |
| 11.10 | No lecture | |
| 17.09 | Discretization of the Poisson Problem in \(R^1\): Theory | LN-3 |
| 18.09 | Discretization of the Poisson Problem in \(R^1\): Implementation | LN-3 |
| 24.09 | FEM for the Poisson Problem in \(R^2\) | LN-4 |
| 25.09 | FEM for the Poisson Problem in \(R^2\) (continnue) | LN-4 |
| 01.10 | No lecture | |
| 02.10 | Abstract FEM: Construction of a Finite Element Space | Chapter 3. in Brenner & Scott |
| 08.10 | Triangular elements | Chapter 3. in Brenner & Scott |
| 09.10 | Triangular elements (continued) | Chapter 3. in Brenner & Scott |
| 15.10 | Quadrilateral Elements | Chapter 3. in Brenner and Scott |
| 16.10 | Summary of Abstract FEM. Lax-Milgram | Chapter 3 in Brenner & Scott. Lax-Milgram. |
| 22.10 | No lecture - Start up phase of programming project | |
| 23.10 | No lecture - Start up phase of programming project | |
| 29.10 | Linear elasticity - Part 1 | |
| 30.10 | Linear elasticity - Part 2 | |
| 12.11 | Convection-Diffusion. Introduction | ER-1 |
| 13.11 | Convection-Diffusion: Example and theory | ER-2 and ER-3 |
| 19.11 | No lecture | |
| 20.11 | Project presentations - Del 1. | |
| 22.11 | Project presentations - Del 2. Deadline for the project. |