Maître de conférences, HdR.
Institut de Modélisation Mathématique de Montpellier UMR CNRS 5149
My PhD dealt with Navier-Stokes equations in thin domains, namely geophysical fluids where the hydrostatic approximation (pression linear along the vertical axis) is in current use, for which I have designed a new mixed finite element, which is stable (see 1). I also proved an existence and convergence theorem for the linearized time-dependent hydrostatic approximation of the Navier-Stokes equations (see 6).In a joint work with Francisco Guillén (Sevilla), (see
I also studied the transport equation, and developed a new variational formulation, useful both theoretically and numerically. It is based on a space-time least squares formulation of the advection equation, which turns it into an anisotropic diffusion equation (see 2,4). To recover the coerciveness, one must work in suitable spaces, and prove a Poincaré-like inequality (see 3,21). This method leads naturally to a space-time finite element discretization which enjoys very good stability properties at any Courant number for pure advection problems (see 2,4).
In collaboration with Eberhard Baensch (Erlangen-Nuremberg), I studied the hydrodynamic features of specific devices used in hematology-haemostasis (see 11).
Currently, I am working on the numerical simulation of coastal erosion,
in the framework of the ANR projects COPTER (Conception Optimisation et Prototypage d'ouvrages de lutte contre l'ERosion en domaine littoral 2006-2008), MATHOCEAN (2009-2012) and OILDEBEACH (2009-2011). With Bijan Mohammadi, I supervised the Ph. D. thesis of Damien Isebe.
(see 12,14,16,17,18,20 ). Damien is now research engineer at
One year POSTDOC POSITION offered in the COPTER project. Start January 2007. Position appointed to Dr Borys Alvarez-Samaniego, extended until july 2008. Later on Borys was research fellow at McMaster University, Ontario.
I supervised with B. Mohammadi the Ph. D. thesis of Afaf Bouharguane, start fall 2008, successfully defended on june 20th, 2011. After a post-doc in Lab. Jean Kuntzmann, University Joseph Fourier, Grenoble, Afaf has now a permanent position of Maitre de conferences in Institut de Mathematiques de Bordeaux, University Bordeaux 1.
A recent topic which I started to investigate is PDE with non local terms, i.e. defined by integrals or in Fourier space. I started to look at the Fowler equation for dune morphodynamics (see 19, 20, 24 ). In a joint work with Mohamed Mellouk, I also studied a stochastic pde (fractional heat equation) (see 13 ). We also applied fractional calculus to signal processing (see 23, 24 ).