(English) Homogeneous multigrid for hybrid discretizations: application to HHO methods
Désolé, cet article est seulement disponible en Anglais Américain.
Catégorie : Nouvelles
A localized orthogonal decomposition strategy for hybrid discontinuous Galerkin methods
Roland Maier： Thursday, 4th April at 11:00 Abstract: We formulate and analyze a multiscale method for an elliptic problem with an oscillatory coefficient based on a skeletal (hybrid) formulation. More precisely, we employ hybrid discontinuous Galerkin approaches and combine them with the localized orthogonal decomposition methodology to obtain a coarse-scale skeletal method that effectively includes fine-scale information. This work is a first step to reliably merge hybrid skeletal formulations and localized orthogonal decomposition and unite the advantages of both strategies. Numerical experiments are presented to illustrate the theoretical findings.
(English) A localized orthogonal decomposition strategy for hybrid discontinuous Galerkin methods
Désolé, cet article est seulement disponible en Anglais Américain.
Modeling some biological phenomena via the porous media approach
Zoubida Mghazli： Thursday, 18rd Jan at 14:00 Abstract Many biological systems can be modeled by the ”porous medium approach”, such as the diffusion of nutrients and other macromolecules through and in biological tissues. In this presentation, after a brief introduction to the ”porous medium approach”, we present some biological systems viewed through this approach. This will mainly concern the process of biodegradation of household waste, the Trichoderma fungi and the flow of water in the plant root.
(English) Modeling some biological phenomena via the porous media approach
Désolé, cet article est seulement disponible en Anglais Américain.
Trilogie sur les éléments finis
La trilogie Éléments Finis a été publiée dans la série Texts in Applied Mathematics de Springer en 2023. Co-écrite par Alexandre Ern de l’équipe SERENA et Jean-Luc Guermond de Texas A&M University, la trilogie comprend trois tomes, traitant de notions fondamentales d’approximation et d’interpolation (tome I), méthodes de Galerkin, EDP elliptiques et mixtes (tome II), et EDP de premier ordre et dépendantes du temps (tome III). Une caractéristique marquante est l’organisation de la trilogie en chapitres relativement petits (de 12 à 14 pages), facilitant ainsi son utilisation comme manuel pour l’enseignement des cours de niveau supérieur et facilitant également son utilisation comme référence pour les chercheurs.
Computer-assisted proofs of radial solutions of elliptic systems on R^d
Olivier Hénot： Thursday 23rd Nov at 11:00 The talk presents recent work on the rigorous computation of localized radial solutions of semilinear elliptic systems. While there are comprehensive results for scalar equations and some specific classes of elliptic systems, much less is known about these solutions in generic systems of nonlinear elliptic equations. These radial solutions are described by systems of non-autonomous ordinary differential equations. Using an appropriate Lyapunov-Perron operator, we rigorously enclose the centre-stable manifold, which contains the asymptotic behaviour of the profile. We then formulate, as a zero-finding problem, a shooting scheme from the set of initial conditions onto the invariant manifold. By means of a Newton-Kantorovich-type theorem, we obtain sufficient conditions to prove the existence and local uniqueness of a zero in the vicinity of a numerical approximation. We apply this method to prove ground state solutions for the Klein-Gordon equation on R^3, the Swift-Hohenberg equation on R^2, and a FitzHugh-Nagumo system on R^2.
(English) Computer-assisted proofs of radial solutions of elliptic systems on R^d
Désolé, cet article est seulement disponible en Anglais Américain.
A Volume-Preserving Reference Map Method for the Level Set Representation
Maxime Theillard： Thursday 16th Nov at 17:00 Abstract: This seminar will present an implicit interface representation, where the geometry is captured by a level set function, and its deformations are reconstructed from the diffeomorphism between the warped and original geometries (the reference map). A key advantage of this representation is that it provides a local estimation of numerical local mass losses. Using this metric, we design a novel projection for the reference map on the space of volume- preserving diffeomorphisms, which results in enhanced but inexact, mass conservation. In the limit of small deviations from this space, the projection is shown to be uniquely defined, and the correction can be computed as the solution of a Poisson problem. The method is analyzed and validated in two and three spatial dimensions. Both the theoretical and computational results show it excels at correcting the mass loss due to inaccuracy in the advection process or the velocity field. This error reduction is particularly impactful for practical applications, such as the simulation of multiphase flows over long time intervals, and offers improved computational exploration capabilities.
(English) A Volume-Preserving Reference Map Method for the Level Set Representation
Désolé, cet article est seulement disponible en Anglais Américain.
