E.D.P.

Description

1) Current spaces : L^2, L^p

2) Sobolev spaces, trace theorem

3) Variational form of a problem

4) Principle of the finite element method

5) Convergence of methods

6) Optimization in infinite dimension

Targeted skills

The student knows how to:

1) discretize partial differential equations by finite elements,

2) use the adjoint method to calculate sensitivities, while controlling numerical errors.

3) program the finite element method on a computer

4) evaluate the computational performance of a software implementation

5) analyze the numerical performance of a solution approach in terms of error

Bibliography

Equations aux dérivées partielles et leurs approximations : Niveau M1, Brigitte Lucquin

Introduction à l'analyse numérique matricielle et à l'optimisation, Patrick Ciarlet

Pre-requisites

Lebesgue integral, linear algebra, optimisation

Session 1 ou session unique - Contrôle des connaissances

Session 2 - Contrôle des connaissances