## 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
Lecture Topics Introduction. FEM-History and FEM applications. Slides Poisson: PDE, Minimization and weak form. LN-1 and Chapter 1. in Quarteroni Mathematical Background. LN-1 and Chapter 2. in Quarteroni Definitions of Lebesgue and Sobolov spaces LN-1 and Chapter 1. in Brenner & Scott Discretization of the Poisson Problem in $R^1$ : Formulation. LN-2 and Sections 3.1 and 3.2 in Quarteroni Discretization of the Poisson problem in $R^1$. Formulation (continue) LN-2 and Section 3.2 in Quarteroni Discretization of the Poisson Problem in $R^1$: Theory LN-3 and Sections 4.1-4.3 in Quarteroni Discretization of the Poisson Problem in $R^1$: Implementation LN-3 FEM for the Poisson Problem in $R^2$ LN-4 and Section 4.4 in Quarteroni FEM for the Poisson Problem in $R^2$ (continnue) LN-4 and Section 4.4 in Quarteroni Abstract FEM: Construction of a Finite Element Space Chapter 3. in Brenner & Scott Triangular elements Chapter 3. in Brenner & Scott Triangular elements (continued) Chapter 3. in Brenner & Scott Quadrilateral Elements Chapter 3. in Brenner and Scott Isoparametric mapping Deformed Geometries, IFEM Ch16 and IFEM Ch17 Adaptive FEM (AFEM): A priori estimates AFEM-notes_TMA4220. Get copies at IMF-office (7th floor SB2) No lecture Adaptive FEM (AFEM): Adaptive refinement AFEM-notes_TMA4220. Get copies at IMF-office (7th floor SB2) Spectrum of Laplace operator Spectrum of Laplace Operator Time-dependent diffusion Time-dependent diffusion Convection-Diffusion. Introduction ER-1 Convection-Diffusion: Theory ER-2 No lecture Convection-Diffusion: Example ER-3 No lecture (Project work) No lecture (Project work) No lecture (Project work) No lecture (Project work)