Numerical Analysis 3

Finite elements are a widely used numerical method. This course will explain the principles of the method, provide useful equations for a variety of problems and give the keys to computer implementation of the method.

Discover the basics of the finite element method and learn about the different types of finite elements (Lagrange, Hermite, Raviart-Thomas, Crouzeix Raviart). Numerous problems (Laplacian, linear elasticity, Stokes, non-conforming problems) will be treated and illustrated numerically using scientific software.

The necessary concepts are developed during the first semester of the course.

Recommended prerequisites: Basic programming skills in scientific software.

An indicative course schedule is as follows:

1) reminder of functional spaces, Lax Milgram's theorem

2) Galerkin's method, principle and important theorems (Céa's lemma, inf sup condition, Strang's lemma)

3) Finite element method in dimension 1: Lagrange finite elements P1, P2, Pk, Hermite finite elements

4) Higher-dimensional finite element method: Lagrangian finite elements P1, Pk, Qk

5) Finite element generation: definitions of different types of finite elements (Lagrange, Hermite (example of use of Argyris elements), Crouzeix Raviart (example of non-conformal approximation), Raviart Thomas)

6) Linear elasticity problem

7) Approximations for mixed problems (Laplacian and Stokes)

Hourly volumes :

            CM: 24 

            TD : 15

            TP:7.5

            Land: 0