Credits

6 ECTS, CTD 36h, TP 18h

• Variational methods applied to modelling
  • ECTS: 6
  • Course code: GBX8AM26 (UGA) or WMM8AM26 (INP)
  • Lecture:
    • ECTS: 3
    • Course code: GBX8AM11 (UGA)
  • Lab:
    • ECTS: 3
    • Course code: GBX8AM06 (UGA)

Instructor

• Clément Jourdana
• Frédérique Charles

Description

The aim of this course is to gain in-depth knowledge of PDE modelling and their numerical resolution, in particular using variational methods such as the Finite Elements method.

Content

1. Introduction to modelling with examples.
2. Boundary problem in 1D, variational formulation, Sobolev spaces.
3. Stationary problem, elliptic equations.
4. Finite element method: algorithm, errors…
5. Evolution models, parabolic equations, splitting methods
6. Extensions and applications, FreeFEM++

This course includes practical sessions.

Prerequisites

Notions of distribution theory, linear algebra, integral calculus, some notions of programming in some high-level language, basic numerical analysis, such as numerical integration of differential equations, basic notions on Hilbert spaces, usual partial differential operators (gradient, divergence, Laplacian…)