Numerical Analysis 3

Finite elements are a widely used numerical method. This course will explain the principles of the method, give the useful equations on various problems and give the keys for the 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 notions are developed during the first semester of the training.

Recommended prerequisites: Programming knowledge on a scientific software.

An indicative program of the course is as follows:

1) reminders on functional spaces, Lax Milgram 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) Finite element method in higher dimension: Lagrange 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 of mixed problems (Laplacian and Stokes)

Hourly volumes:

            CM : 24 

            TD : 15

            TP :7,5

            Land : 0