Research

I am interested in the development and the convergence analysis of linear and nonlinear efficient numerical methods enabling the resolution and preserving the physical properties of partial differential equations.

Keywords

degenerate parabolic equations, finite volumes, gradient schemes, nonlinear schemes, positivity, asymptotic preserving schemes, thermistor problems, multiphase flows, anisotropic diffusion, fractured porous media, image processing, modeling.

Main applications

  • Geothermal energy

  • Petroleum engineering

  • Biological processes : chemotaxis & Pattern formation

  • Prediction of bio-sourced material properties

Research visits

  • Visit to School of Mathematical Sciences, Monash University, Melbourne, Australia
    Invited by Prof. Jérôme Droniou from November 7 to December 10, 2019. This research stay has been about the investigation of the key elements allowing the convergence of Two-Point Flux Approximation (TPFA) scheme for a heterogeneous two-phase flow problem in porous media with buoyancy and discontinuous capillarity.