Numerical integration of Partial Differential Equations,
especially of hyperbolic type. Models of mathematical physics.

- Finite difference and finite volume methods for conservation and
balance laws, with particular emphasis on high order methods,
stiff problems and on the
preservation of equilibrium solutions.
- Kinetic models: Models for mixture of gases, Polyatomic gases,
Traffic models.
- Methods for kinetic problems: noise reduction for Monte Carlo
methods, domain
decomposition and multiscale methods, numerical integration of
simplified models, such as the BGK equation.
- Adaptive and multiscale methods: a-posteriori error indicator
based on entropy production for hyperbolic problems, domain
decomposition methods for kinetic models. Preservation of
asymptotic and equilibrium states in numerical schemes.
- Relaxation methods for systems of equations.
- Spectral methods and finite element methods: stabilization of convection
diffusion equations.
- Vortex methods for incompressible equations.

She authors or co-authors more than fifty
scientific publications, appeared on the best international journals of the field: J. Comp. Phys,
SIAM J. Scientific Computing, J. Scientific Computing, SIAM J. of Numerical Analysis, Communications in Computational
Physics, Math. of Comp., Computers and Fluids, Kinetics and
Related Models, Communications in Math. Sciences.