- 4MMMVAM

Goal(s)

To deepen knowledges on mathematical modeling with PDEs and their numerical resolution. We present mainly finite element methods whose theoretical aspects, numerical schemes and programming issues are studied.

Responsible(s)

Clément JOURDANA

Content(s)

I - Introduction to modeling through some examples: heat transfer (1D/2D, Steady/Transient), transport, elasticity (Lamé), fluid (Stokes), fluid-structure coupling (flow around an elastic obstacle). Comments on specific mathematical issues of above problems.
II - Boundary value problems and weak formulations.
III - Steady-state models / elliptic equations
Variationnal context. Symmetrical case and minization. Green formulaes.
IV - Finite elements method: basis functions, algorithms, implementation, a-priori estimates. Transport term, stabilization. Non linear case : linearization.
III - Unsteady models / Parabolic equations
Time scheme, splitting methods. FD-FE schemes.

2nd year course, first semester "Partial differential equations and finite difference method"
1st year course 3MMBMI

This course is taught in English.

Test

Evaluation : 30% of TP et projets notés + examens écrits et oraux and 70% of Examen écrit (2h)

Resit : 30% of TP et projets notés + examens écrits et oraux (reported score) and 70% of Examen écrit (2h)

The exam is given in english only

Calendar

The course exists in the following branches:

• Curriculum - Core curriculum - Semester 8 (this course is given in english only)

Additional Information

Course ID : 4MMMVAM
Course language(s):

You can find this course among all other courses.

Bibliography

G. ALLAIRE, Analyse numérique et optimisation, Edts de l’école polytechnique, 2006.
G. ALLAIRE, Numerical analysis and optimization: an introduction to mathematical modeling and numerical simulation, Oxford university press, 2007.
A. Ern, J.-L. Guermond, Theory and practice of finite elements, Vol. 159, Springer Science & business Media, 2013.
A. QUARTERONI and A. VALLI : « Numerical approximation of PDEs », Springer, 1994.
P.-A. RAVIART et J.-M. THOMAS : Introduction à l'analyse numérique des équations aux dérivées partielles, Coll. Mathématiques appliquées pour la Maîtrise, Dunod, 2004.