Modul: MAT075 Zurich Graduate Colloquium

## What are... numerical schemes for conservation laws?

Élise Delphine Le Mélédo talk

**Date:** 19.02.19 **Time:** 17.15 - 18.30 **Room:**

Lot of natural phenomenon can be modelled and investigated through the so-called problems of conservation laws, where the time-space dynamics preserves quantities such motion, energy and mass.

Their analytical solution (if any) is most of the time unknown. Therefore, we have to apply numerical methods that are paying attention to the physical quantities preserved through the dynamic. Another main challenge for constructing those methods is coming from the theory where discontinuities are developing within the solution. Thus, weak solutions are required and paying a special attention to the conservation laws is primordial.

If this concern traces back to the 20's, the numerical solvers commonly used nowadays in applications are still lacking efficiency, preferring stability to high performance. We focus on improving existing high order schemes by involving theoretical results in their construction and design new ones by combining general techniques with the known properties of those problems.