# Coursebooks

## Numerics for fluids, structures & electromagnetics

English

#### Remark

pas donné en 2020-21

#### Summary

The aim of the course is to give a theoretical and practical knowledge of the finite element method for saddle point problems, such as fluid dynamics, elasticity and electromagnetic problems.

#### Keywords

Partial differential equations,  saddle point problems, finite element method, Galerkin approximation, stability and convergence analysis.

#### Learning Prerequisites

##### Required courses

Analysis I II III IV, Numerical Analysis, Advanced numerical analysis, Sobolev spaces and elliptic equations, Numerical Approximations of PDEs

##### Important concepts to start the course

• Basic knowledge of functional analysis: Banach and Hilbert spaces, L^p spaces.
• Some knowledge on theory of PDEs: classical and weak solutions, existence and uniqueness.
• Basic concepts in numerical analysis: stability, convergence, condition number, solution of linear systems, quadrature formulae, finite difference formulae, polynomial interpolation.
• Basic information on finite element theory for elliptic problems

#### Learning Outcomes

By the end of the course, the student must be able to:
• Identify features of a PDE relevant for the selection and performance of a numerical algorithm.
• Assess / Evaluate numerical methods in light of the theoretical results.
• Implement numerical methods for saddle point problems
• Choose an appropriate method to solve a given differential problem
• Prove convergence of a discretisation scheme

#### Transversal skills

• Write a scientific or technical report.

#### Teaching methods

Ex cathedra lectures, exercises in the classroom and computer lab sessions.

#### Expected student activities

• Attendance of lectures.
• Completing exercises.
• Solving problems with an academic software as Free FEM ++

#### Assessment methods

Oral exams and evaluation of the report of a mini-project.

#### Supervision

 Office hours Yes Assistants Yes Forum No

#### Resources

##### Bibliography

• S.C. Brenner, L.R. Scott. The Mathematical Theory of Finite Element Methods. Springer 2007.
• A. Ern, J-L. Guermond, Theory and Practice of Finite Elements. Springer 2004.
• D. Boffi, F. Brezzi, M. Fortin Mixed Finite elements and Applications, Springer Verlag. 2013.

##### Notes/Handbook

Notes for each lectures will be provided every week.

### Reference week

MoTuWeThFr
8-9
9-10
10-11
11-12
12-13
13-14
14-15
15-16
16-17
17-18
18-19
19-20
20-21
21-22
Under construction

Lecture
Exercise, TP
Project, other

### legend

• Autumn semester
• Winter sessions
• Spring semester
• Summer sessions
• Lecture in French
• Lecture in English
• Lecture in German