## 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:** Monday and Thursday.

The topics will be described as we proceed.

Lecture | Topics | Reading | |
---|---|---|---|

17.08 | Introduction. FEM-History and FEM applications. | Slides | |

20.08 | Poisson: PDE, Minimization and weak form. | LN-1 and Chapter 1. in Quarteroni | |

24.08 | Mathematical Background. | LN-1, Chapter 2. in Quarteroni, and Chapter 1. in Brenner& Scott | |

27.08 | Definitions of Lebesgue and Sobolov spaces | LN-1 and Chapter 1. in Brenner & Scott | |

31.08 | Discretization of the Poisson Problem in \(R^1\) : Formulation. | LN-2 and Sections 3.1 and 3.2 in Quarteroni | |

03.09 | Discretization of the Poisson problem in \(R^1\). Formulation (continue) | LN-2 and Section 3.2 in Quarteroni | |

07.09 | Discretization of the Poisson Problem in \(R^1\): Theory | LN-3 and Sections 4.1-4.3 in Quarteroni | |

10.09 | No lecture | ||

14.09 | Discretization of the Poisson Problem in \(R^1\): Implementation | LN-3 | |

17.09 | FEM for the Poisson Problem in \(R^2\) | LN-4 and Section 4.4 in Quarteroni | |

21.09 | FEM for the Poisson Problem in \(R^2\) (continnue) | LN-4 and Section 4.4 in Quarteroni | |

24.09 | Abstract FEM: Construction of a Finite Element Space | Chapter 3. in Brenner & Scott | |

28.09 | Triangular elements | Chapter 3. in Brenner & Scott | |

01.10 | Triangular elements (continued) | Chapter 3. in Brenner & Scott | |

05.10 | Quadrilateral Elements | Chapter 3. in Brenner and Scott | |

08.10 | Isoparametric mapping | Deformed Geometries, IFEM Ch16 and IFEM Ch17 | |

12.10 | Adaptive FEM (AFEM): A priori estimates | AFEM-notes_TMA4220. (See Blackboard) | |

15.10 | Adaptive FEM (AFEM): A posteriori estimates | AFEM-notes_TMA4220. (See Blackboard) | |

19.10 | Adaptive FEM (AFEM): Adaptive refinement | AFEM-notes_TMA4220. (See Blackboard) | |

22.10 | Spectrum of Laplace operator | Spectrum of Laplace Operator | |

26.10 | Time-dependent diffusion | Time-dependent diffusion | |

29.10 | Convection-Diffusion. Introduction | ER-1 | |

02.11 | Convection-Diffusion: Example | ER-2 | |

05.11 | Convection-Diffusion: Theory | ER-3 | |

09.11 | No lecture (Project work) | ||

12.11 | No lecture (Project work) | ||

16.11 | No lecture (Project work) | ||

19.11 | No lecture (Project work) |