(Français) Computable reliable bounds for Poincaré–Friedrichs constants via Čech–de-Rham complexes
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Computable reliable bounds for Poincaré–Friedrichs constants via Čech–de-Rham complexes
Martin Licht: Thursday, 25th April at 11:00 Abstract: We derive computable and reliable upper bounds for Poincaré–Friedrichs constants of classical Sobolev spaces and, more generally, Sobolev de-Rham complexes. The upper bounds are in terms of local Poincaré–Friedrichs constants over subdomains and the smallest singular value of a finite-dimensional operator that is easily assembled from the geometric setting. Thus we reduce the computational effort when computing the Poincaré–Friedrichs constant of finite de-Rham complexes, and we provide computable reliable bounds even for the original Sobolev de-Rham complex. The reduction to a finite-dimensional system uses diagram chasing within a Čech–de-Rham complex.
(Français) Homogeneous multigrid for hybrid discretizations: application to HHO methods
Sorry, this entry is only available in French.
Homogeneous multigrid for hybrid discretizations: application to HHO methods
Andreas Rupp： Tuesday, 2nd April at 14:00 Abstract: We prove the uniform convergence of the geometric multigrid V-cycle for hybrid high-order (HHO) and other discontinuous skeletal methods. Our results generalize previously established results for HDG methods, and our multigrid method uses standard smoothers and local solvers that are bounded, convergent, and consistent. We use a weak version of elliptic regularity in our proofs. Numerical experiments confirm our theoretical results.
(Français) A localized orthogonal decomposition strategy for hybrid discontinuous Galerkin methods
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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.
(Français) Modeling some biological phenomena via the porous media approach
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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.
Finite element trilogy
The Finite Element trilogy was published in the Series Texts in Applied Mathematics by Springer in 2023. Co-authored by Alexandre Ern from the SERENA Team and Jean-Luc Guermond from Texas A&M University, the trilogy comprises three volumes, dealing with fundamental notions of approximation and interpolation (volume I), Galerkin methods, elliptic and mixed PDEs (volume II), and first-order and time-dependent PDEs (volume III). A salient feature is the organization of the trilogy in relatively small chapters (from 12 to 14 pages), thereby facilitating its use as a textbook for teaching graduate level courses and also easing its use as a reference for researchers.
IFPEN / Inria meeting
Journée contrat cadre IFPEN / Inria 2023
