The project-team RAPSODI is a mixed research team between Inria, Université de Lille, and CNRS.

RAPSODI members are part of the Numerical Analysis and Partial Differential Equations (ANEDP) team of the Paul Painlevé laboratory (mixed Université de Lille/CNRS unity).


The activity of the team is devoted to the design, the analysis, and the efficient implementation of numerical schemes for dissipative models arising in physics or biology. We particularly focus our attention on the preservation of some physical characteristics at the discrete level: positivity, mass conservation, growth of physical entropies, asymptotic behaviors… We also aim at optimizing the computational cost at fixed accuracy, by developing high-order schemes, or by the mean of a posteriori error control. Finally, we adapt the algorithms to the potential industrial constraints, so that they can be incorporated in existing codes.


Research interests

  • Mathematical topics:
    • theoretical and numerical analysis of partial differential equations
    • finite volume and finite element schemes
    • high-order methods, spectral methods
    • a posteriori error control
    • asymptotic-preserving schemes
  • Application fields:
    • porous media flows
    • complex fluid mechanics
    • corrosion
    • electromagnetism
    • semiconductor devices, metamaterials
    • plasma physics


  • Industrial partners:
  • Academic partners:
    • Université Pierre et Marie Curie (Paris, France)
    • Université de Nice – Sophia Antipolis (France)
    • Université de Nantes (France)
    • Université de Montpellier (France)
    • Université François Rabelais (Tours, France)
    • Université Paul Sabatier (Toulouse, France)
    • Aix-Marseille Université (France)
    • T. U. Eindhoven (The Netherlands)
    • T. U. Vienna (Austria)
    • Monash University (Melbourne, Australia)
    • École Polytechnique Fédérale de Lausanne (Switzerland)
    • University of Monastir (Tunisia)
    • Unicamp (Campinas, Brazil)
    • Imperial College London (UK)

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