MATH-468 / 5 credits

Teacher:

Language: English

Remark: Pas donné en 2024-25. Cours donné en alternance tous les deux ans.

## Summary

Cours donné en alternance tous les deux ans

## Keywords

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

## Required courses

Analysis I II III IV, Numerical Analysis,  Numerical Approximations of PDEs

## Recommended courses

Sobolev spaces and elliptic equations,

## 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.
• Make an oral presentation.

## 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 ++

Oral

## Supervision

 Office hours Yes Assistants Yes Forum Yes

## 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.

## In the programs

• Semester: Fall
• Exam form: Oral (winter session)
• Subject examined: Numerics for fluids, structures & electromagnetics
• Lecture: 2 Hour(s) per week x 14 weeks
• Exercises: 2 Hour(s) per week x 14 weeks
• Type: optional
• Semester: Fall
• Exam form: Oral (winter session)
• Subject examined: Numerics for fluids, structures & electromagnetics
• Lecture: 2 Hour(s) per week x 14 weeks
• Exercises: 2 Hour(s) per week x 14 weeks
• Type: optional
• Semester: Fall
• Exam form: Oral (winter session)
• Subject examined: Numerics for fluids, structures & electromagnetics
• Lecture: 2 Hour(s) per week x 14 weeks
• Exercises: 2 Hour(s) per week x 14 weeks
• Type: optional
• Semester: Fall
• Exam form: Oral (winter session)
• Subject examined: Numerics for fluids, structures & electromagnetics
• Lecture: 2 Hour(s) per week x 14 weeks
• Exercises: 2 Hour(s) per week x 14 weeks
• Type: optional
• Semester: Fall
• Exam form: Oral (winter session)
• Subject examined: Numerics for fluids, structures & electromagnetics
• Lecture: 2 Hour(s) per week x 14 weeks
• Exercises: 2 Hour(s) per week x 14 weeks
• Type: optional
• Semester: Fall
• Exam form: Oral (winter session)
• Subject examined: Numerics for fluids, structures & electromagnetics
• Lecture: 2 Hour(s) per week x 14 weeks
• Exercises: 2 Hour(s) per week x 14 weeks
• Type: optional
• Semester: Fall
• Exam form: Oral (winter session)
• Subject examined: Numerics for fluids, structures & electromagnetics
• Lecture: 2 Hour(s) per week x 14 weeks
• Exercises: 2 Hour(s) per week x 14 weeks
• Type: optional
• Semester: Fall
• Exam form: Oral (winter session)
• Subject examined: Numerics for fluids, structures & electromagnetics
• Lecture: 2 Hour(s) per week x 14 weeks
• Exercises: 2 Hour(s) per week x 14 weeks
• Type: optional

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