Numerical methods for time-dependent PDE
M2 - B004
Description
Numerical methods for evolutionary partial differential equations (PDEs) can be considered to be based on two pillars. The first pillar is the functional analysis and the theory of functional spaces, the second pillar is based on PDE models and their links with the modeling of real phenomena. This discipline is also closely linked to the development of computer calculation means.
However, the construction and numerical analysis of efficient numerical methods for evolutionary PDEs are based on their own rules which are the subject of this basic course.
Contents
- Models and functional framework.
- Construction of numerical methods in 1D and 2D: Finite Differences, Finite Volumes and comparison with Finite Elements.
- Convergence of Finite Differences: stability, consistency, convergence and Lax theorem.
- Applications: transport, non uniform mesh, low regularity data, semi-lagrangian schemes.
- Convergence of Finite Volumes (in 2D) for transport and for diffusion: H1 or BV data.
- Non linear schemes: TVD criterion and convergence for transport.
Lecture notes
Lecture notes by Bruno Després