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 08:15-10:00 and Thursday 12:15-14:00.
The topics will be described as we proceed.

Lecture Topics Reading
24.08 Introduction. FEM-History and FEM applications. Slides
26.08 Poisson: PDE, Minimization and weak form. LN-1 and Chapter 1. in Quarteroni
31.08 Mathematical Background.
LN-1, Chapter 2. in Quarteroni, and Chapter 1. in Brenner& Scott
02.09 Definitions of Lebesgue and Sobolov spaces LN-1 and Chapter 1. in Brenner & Scott
07.09 Discretization of the Poisson Problem in \(R^1\) : Formulation. LN-2 and Sections 3.1 and 3.2 in Quarteroni
09.09 Discretization of the Poisson problem in \(R^1\). Formulation (continue) LN-2 and Section 3.2 in Quarteroni
14.09 Discretization of the Poisson Problem in \(R^1\): Theory LN-3 and Sections 4.1-4.3 in Quarteroni
16.09 Discretization of the Poisson Problem in \(R^1\): Implementation LN-3
21.09 No lecture
23.09 FEM for the Poisson Problem in \(R^2\) LN-4 and Section 4.4 in Quarteroni
28.09 FEM for the Poisson Problem in \(R^2\) (continnue) LN-4 and Section 4.4 in Quarteroni
30.09 No lecture
04.10 Abstract FEM: Construction of a Finite Element Space Chapter 3. in Brenner & Scott
05.10 Triangular elements Chapter 3. in Brenner & Scott
07.10 No lecture
11.10 Triangular elements (continued) Chapter 3. in Brenner & Scott
12.10 Quadrilateral Elements Chapter 3. in Brenner and Scott
14.10 Isoparametric mapping Deformed Geometries, IFEM Ch16 and IFEM Ch17
18.10 Adaptive FEM (AFEM): A priori estimates AFEM-notes_TMA4220. (See Blackboard)
19.10 No lecture
21.10 No lecture
25.10 Adaptive FEM (AFEM): A posteriori estimates AFEM-notes_TMA4220. (See Blackboard)
26.10 Adaptive FEM (AFEM): Adaptive refinement AFEM-notes_TMA4220. (See Blackboard)
28.10 Spectrum of Laplace operator Spectrum of Laplace Operator
01.11 Time-dependent diffusion Time-dependent diffusion
02.11 Convection-Diffusion. Introduction ER-1
04.11 Convection-Diffusion: Example and Theory ER-2, ER-3
08.11 No lecture
09.11 No lecture
11.11 No lecture
2021-11-07, Trond Kvamsdal