M2 MF — Numerics for transport

The lecture will be given during fall 2023 for the students of the Master 2 in Fundamental Mathematics (french website). The first session takes place on Tuesday, November 7. 2023.

Abstract

This course is the numerical counterpart of the Hyperbolic Equations course, given by Miguel Rodrigues in parallel. A first part will focus on the analysis of finite difference schemes. The issues of stability and consistency for such schemes considered in the infinite or periodic domain as well as in the bounded domain will be addressed. Secondly, the approximation of entropy weak solutions of non-linear hyperbolic conservation laws will be studied through the construction and analysis of the finite volume method. Recent developments of such schemes will be discussed.

Selected references

• Strikwerda JC (2004) Finite difference schemes and partial differential equations, 2nd ed., Philadelphia, PA: Society for Industrial and Applied Mathematics (SIAM). DOI
• Gustafsson B, Kreiss H-O, Oliger J (2013) Time-dependent problems and difference methods, John Wiley & Sons, Inc., Hoboken, NJ. DOI
• LeVeque RJ (2002) Finite Volume Methods for Hyperbolic Problems, Cambridge University Press, Cambridge. DOI
• Bouchut F (2004) Nonlinear stability of finite volume methods for hyperbolic conservation laws and well-balanced schemes for sources, Birkhäuser. DOI

Technical informations

Evaluation schedule

• CC1 on Friday December 1st
• CC2 on Thursday December 21

Numerical experiments

• November 28 / download the jupyter notebook / notebook with correction / html correction
• December 12.