Section: New Results

Two-Scale numerical methods

Participant : E. Frénod.

In note [39] a classification of Homogenization-Based Numerical Methods and (in particular) of Numerical Methods that are based on the Two-Scale Convergence is done. In this classification stand: Direct Homogenization-Based Numerical Methods, H-Measure-Based Numerical Methods, Two-Scale Numerical Methods and TSAPS (Two-Scale Asymptotic Preserving Schemes).

In [34] we develop and we explain the two-scale convergence in the covariant formalism, i.e. using differential forms on a Riemannian manifold. For that purpose, we consider two manifolds M and Y, the first one contains the positions and the second one the oscillations. We establish some convergence results working on geodesics on a manifold. Then, we apply this framework on examples.