Coursebooks 2017-2018

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Numerical methods for saddle point problems

MATH-468

Lecturer(s) :

Buffa Annalisa

Language:

English

Summary

The aim of the course is to give a theoretical and practical knowledge of the finite element method for saddle point problems.

Content

- Minimization of convex functionals (energies) under linear constraints and their interpretation as saddle point problems. Wellposedness and inf-sup conditions.

- Finite element approximation of saddle point problems, discrete inf-sup conditions, stability and approximation estimates

- Finite elements for Stokes flows, (quasi-)incompressible linear elasticity, and Darcy flows

- Compatible discretisations of differential forms and of Maxwell equations

 

 

Keywords

Finite element methods, Galerkin approximation, mixed finite elements, Darcy flows, incompressible fluids and linear elasticity, Maxwell equations, discrete differential forms.

Learning Prerequisites

Required courses

Analysis I II III IV, Numerical Analysis, Advanced numerical analysis, Sobolev spaces and elliptic equations.

Recommended courses

Functional analysis I, measure and integration, Programming 

 

Important concepts to start the course

- Basic knowledge of functional analysis, Banach and Hilbert spaces, L^p spaces

- Some knowledge on the theory of elliptic PDEs, weak solutions, existence and uniqueness

- Basic concepts in numerical analysis: stability, convergence, condition number, solution of linear systems, quadrature formulae, polynomial interpolation.

 

Learning Outcomes

By the end of the course, the student must be able to:

Transversal skills

Teaching methods

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

Expected student activities

- Attendance of lectures 

- Completing exercises

- Solving problems on the computer

- Work out a small project and write a technical report 

Assessment methods

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

Dans le cas de l'art. 3 al. 5 du Règlement de section, l'enseignant décide de la forme de l'examen qu'il communique aux étudiants concernés.

Supervision

Office hours No
Assistants Yes

Resources

Bibliography

- D. Boffi, F. Brezzi, M. Fortin Mixed Finite Element Methods and Applications, Springer Series in Computatioanl mathematics, 2013. 

- P. Monk, Finite Element Methods for Maxwell Equations, Oxford University press, 2003

- A. Ern, J-L. Guermond, Theory and Practise of Finite Elements, Springer 2004.

Ressources en bibliothèque
Moodle Link

In the programs

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

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