Maître de conférences, HdR, hors-classe.
Institut Montpellierain Alexander Grothendieck UMR CNRS 5149
My early research 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).
I also worked 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
From January 2007 to july 2008 I supervised Dr Borys Alvarez-Samaniego post-doc in the COPTER project. Borys is now in the Central University of Ecuador, Quito.
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.
I formally supervised with F. Marche the Ph. D. of Arnaud Duran, start fall 2011, successfully defended on october 17th, 2014. Arnaud has now a permanent position of Maitre de conferences in Institut Camille Jordan, University Lyon 1.
I also investigated some 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 ).