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: Theory ER-2
05.11 Convection-Diffusion: Example 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)
2020-10-11, Trond Kvamsdal