Numerical Analysis 3

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

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

The necessary concepts are developed during the first semester of the training program.

Recommended prerequisites: Basic programming skills using scientific software.

An indicative program for the course is as follows:

1) Reminders about functional spaces, Lax-Milgram theorem

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

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

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

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

6) Problem of linear elasticity

7) Approximations of mixed problems (Laplacian and Stokes)

Hourly volumes:

            CM: 24 

            TD: 15

            TP: 7.5

            Land: 0