UE Variational methods applied to modelling

The aim of this course is to get deep 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 include practical sessions.

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