Advanced finite element numerical simulation

Competencies
- Know how to construct a variational formulation for a problem in mechanics of continuous media, fluids (Stokes) or deformable solids (elasticity).
- Know some classical finite elements in dimension 2 and 3 (Lagrange Pk, isoparametric Qk, bubble element for Stokes...) and their approximation properties, know how to choose the element according to the application.
- Understand the implementation of a finite element code on unstructured mesh. Understand how to implement a finite element code on an unstructured mesh.
Course content
1. Variational formulations in continuum mechanics:
- Stokes equations
- linear elasticity
2. Finite element method:
- reminders of the principle of the method (Galerkin's method, definition of a unisolvent element)
- unstructured meshes and construction of approximation spaces
- general principle of linear system construction
3. Implementation:
- representation of meshes
- principle of matrix assembly procedures
- calculation of elementary matrices by passing to the reference element
Course outline
First part: "lectures" briefly reviewing the 3 points above.
Second part: realization of a project dedicated either to the complete programming of a solver, or to the use of Freefem++ to solve and explore a complex problem, or to a theoretical study of numerical analysis.

First part: lectures briefly recalling the 3 points above.
Second part: realization of a project dedicated either to the complete programming of a solver, or to the use of Freefem++ to solve and explore a complex problem, or to a theoretical study of numerical analysis.