Our team has made several contributions in the description of the limit behaviour, as the mesh sizes tend to zero, of numerical schemes for wave and Schrödinger equations from a control theoretical perspective. These results show that, in particular, filtering the high frequency numerical spurious solutions is necessary (and a good remedy) to assure the convergence of numerical schemes from a control perspective. These results also provide insight into the link between conservative finite and infinite-dimensional dynamical systems and their asymptotic behaviour.
Guidance by repulsion model describing the behaviour of two agents, a driver and an evader
Various numerical approximation methods are discussed with the aim of recoving the large time asymptotic properties of the hypoelliptic Kolmogorov model