The scientific topics of the team “Modeling, Analysis and Simulation” focus on the mathematical study, numerical analysis and simulation of equations from physics and mechanics. Application domains include

- Molecular and multiscale simulation with in particular the coupling between models at the microscopic scale (quantum and statistical physics) and models at the macroscopic scale. A broad range of mathematical tools are used: analysis of partial differential equations, spectral analysis, stochastic processes, variational methods, etc.
- Fluid and solid mechanics for which mathematical models and numerical methods at a more macroscopic scale are developed. The research efforts are for instance directed towards finite element methods, discontinuous Galerkin techniques, hybrid high-order (HHO) methods, a posteriori error estimates and unfitted mesh techniques for interface problems.
- PDEs and materials, with in particular the study of dislocation dynamics and free surface problems.
- The control and stabilization of partial differential equations.

The permanent researchers of the team are Etienne Bernard, Eric Cancès, Virginie Ehrlacher, Alexandre Ern, Amaury Hayat, Claude Le Bris, Tony Lelièvre, Pierre Lissy, Régis Monneau, Gabriel Stoltz, and Urbain Vaes.