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- English
Fiches de cours
Numerics for fluids, structures & electromagnetics
MATH-468
Enseignant(s) :
Langue:
English
Remark
pas donné en 2020-21Summary
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.Content
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.
Ressources en bibliothèque
- The Mathematical Theory of Finite Element Methods / S.C. Brenner & L.R. Scott
- Mixed Finite elements and Applications / D. Boffi, F. Brezzi & M. Fortin
- Theory and Practice of Finite Elements / A. Ern & J-L. Guermond
Notes/Handbook
Notes for each lectures will be provided every week.
Dans les plans d'études
- SemestrePrintemps
- Forme de l'examenOral
- Crédits
5 - Matière examinée
Numerics for fluids, structures & electromagnetics - Cours
2 Heure(s) hebdo x 14 semaines - Exercices
2 Heure(s) hebdo x 14 semaines
- Semestre
- SemestrePrintemps
- Forme de l'examenOral
- Crédits
5 - Matière examinée
Numerics for fluids, structures & electromagnetics - Cours
2 Heure(s) hebdo x 14 semaines - Exercices
2 Heure(s) hebdo x 14 semaines
- Semestre
- SemestrePrintemps
- Forme de l'examenOral
- Crédits
5 - Matière examinée
Numerics for fluids, structures & electromagnetics - Cours
2 Heure(s) hebdo x 14 semaines - Exercices
2 Heure(s) hebdo x 14 semaines
- Semestre
- SemestrePrintemps
- Forme de l'examenOral
- Crédits
5 - Matière examinée
Numerics for fluids, structures & electromagnetics - Cours
2 Heure(s) hebdo x 14 semaines - Exercices
2 Heure(s) hebdo x 14 semaines
- Semestre
- SemestrePrintemps
- Forme de l'examenOral
- Crédits
5 - Matière examinée
Numerics for fluids, structures & electromagnetics - Cours
2 Heure(s) hebdo x 14 semaines - Exercices
2 Heure(s) hebdo x 14 semaines
- Semestre
Semaine de référence
Lu | Ma | Me | Je | Ve | |
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8-9 | |||||
9-10 | MAA112 | ||||
10-11 | |||||
11-12 | MAA112 | ||||
12-13 | |||||
13-14 | |||||
14-15 | |||||
15-16 | |||||
16-17 | |||||
17-18 | |||||
18-19 | |||||
19-20 | |||||
20-21 | |||||
21-22 |
Cours
Exercice, TP
Projet, autre
légende
- Semestre d'automne
- Session d'hiver
- Semestre de printemps
- Session d'été
- Cours en français
- Cours en anglais
- Cours en allemand