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Séminaire Equations aux dérivées partielles

organisé par l'équipe Modélisation et contrôle

  • Annamaria Massimini

    Structure-preserving hybrid finite volume scheme for an anisotropic cross-diffusion system

    12 mai 2026 - 14:00Salle de séminaires IRMA

    In this presentation, I will introduce a hybrid finite volume method on general polygonal and polyhedral meshes for the modeling of an anisotropic cross-diffusion system arising from a mesoscopic stochastic process describing diffusion in solids, under a size-exclusion constraint.
    This system possesses an entropy structure, which is exploited to define the numerical scheme in terms of (discrete) entropy variables, and is thus preserved at the discrete level.
    This structure makes it possible to prove the existence of nonnegative discrete solutions satisfying the size-exclusion constraint, as well as mass conservation, and to establish the convergence of the scheme under mesh refinement.
    To the best of our knowledge, this is the first work proposing and analyzing a structure-preserving hybrid finite volume scheme for anisotropic cross-diffusion systems on general polygonal and polyhedral meshes.

    The preprint associated with this presentation is:
    V. Ehrlacher, A. Massimini, J. Moatti. Structure-preserving hybrid finite volume scheme for an anisotropic cross-diffusion system, 2026. Preprint, HAL : hal-05589824

  • Lukas Renelt

    Optimal contraction of the energy difference in adaptive FEM for strongly monotone nonlinear problems

    19 mai 2026 - 14:00Salle de conférences IRMA

    In this talk we discuss the convergence of adaptive FEM for strongly monotone nonlinear partial differential equations arising from the minimization of a convex energy functional. Rather than focusing on specific algorithmic implementations, we establish a generalized theoretical framework that identifies sufficient conditions for an adaptive scheme to contract the energy difference at an optimal rate relative to the number of degrees of freedom. The presented abstract point of view is subsequently shown to include many existing error estimation approaches (local residuals, flux equilibration, linear residual liftings, energy descent), thereby providing a unified proof for their optimal convergence. A key contribution of our recent work is the introduction of computable local equivalence factors yielding a computable a posteriori bound on the contraction rate which can then be used for an improved local refinement procedure. Finally, we will discuss technical challenges posed by higher-order discretizations and show how the arising oscillations can be managed through local higher-order flux-equilibration.

  • Teresa Malheiro Et Gaspar Machado

    TBA

    26 mai 2026 - 14:00A confirmer