396 citations
Counting papers with at most 25 authors, so collaboration author lists do not stand in for the people here.
- Centre National de la Recherche ScientifiqueFR154 papers
- Paris-Est SupFR126 papers
- École nationale des ponts et chausséesFR92 papers
- CERMICSFR71 papers
- Institut national de recherche en sciences et technologies du numériqueFR64 papers
- Laboratoire d'Informatique Gaspard-MongeFR46 papers
- Laboratoire d’Analyse et de Mathématiques AppliquéesFR44 papers
- Université Paris-Est CréteilFR40 papers
- Université Paris-Est Marne-la-ValléeFR39 papers
- Laboratoire NavierFR33 papers
- Laboratoire Modélisation et Simulation Multi-EchelleFR29 papers
- Université Paris DiderotFR15 papers
29 papers · 1 filter
Uniform-in-time convergence of numerical methods for non-linear degenerate parabolic equations
Jerome Droniou, Robert Eymard
Gradient schemes is a framework that enables the unified convergence analysis of many numerical methods for elliptic and parabolic partial differential equations: conforming and no…
An adaptive stabilized conforming finite element method via residual minimization on dual discontinuous Galerkin norms
Victor M. Calo, Alexandre Ern, Ignacio Muga +1
We design and analyze a new adaptive stabilized finite element method. We construct a discrete approximation of the solution in a continuous trial space by minimizing the residual…
Guaranteed and robust -norm a posteriori error estimates for 1D linear advection problems
Alexandre Ern, Martin Vohralík, Mohammad Zakerzadeh
We propose a reconstruction-based a posteriori error estimate for linear advection problems in one space dimension. In our framework, a stable variational ultra-weak formulation is…
A Hybrid High-Order method for the incompressible Navier--Stokes equations based on Temam's device
Lorenzo Botti, Daniele Di Pietro, Jérôme Droniou
In this work we propose a novel Hybrid High-Order method for the incompressible Navier--Stokes equations based on a formulation of the convective term including Temam's device for…
A posteriori error estimation and adaptive strategy for PGD model reduction applied to parametrized linear parabolic problems
Ludovic Chamoin, Florent Pled, Pierre-Eric Allier +1
We define an a posteriori verification procedure that enables to control and certify PGD-based model reduction techniques applied to parametrized linear elliptic or parabolic probl…
Low-rank approximation of linear parabolic equations by space-time tensor Galerkin methods
Thomas Boiveau, Virginie Ehrlacher, Alexandre Ern +1
We devise a space-time tensor method for the low-rank approximation of linear parabolic evolution equations. The proposed method is a stable Galerkin method, uniformly in the discr…
A Hybrid High-Order method for highly oscillatory elliptic problems
Matteo Cicuttin, Alexandre Ern, Simon Lemaire
We devise a Hybrid High-Order (HHO) method for highly oscillatory elliptic problems that is capable of handling general meshes. The method hinges on discrete unknowns that are poly…
A finite element implementation of the isotropic exponentiated Hencky-logarithmic model and simulation of the eversion of elastic tubes
Boumediene Nedjar, Herbert Baaser, Robert J. Martin +1
We investigate a finite element formulation of the exponentiated Hencky-logarithmic model whose strain energy function is given by \[ W_\mathrm{eH}(\boldsymbol{F}) = \dfracμ{k}\, e…
A multiscale method for semi-linear elliptic equations with localized uncertainties and non-linearities
Anthony Nouy, Florent Pled
A multiscale numerical method is proposed for the solution of semi-linear elliptic stochastic partial differential equations with localized uncertainties and non-linearities, the u…
Equilibrated flux a posteriori error estimates in -norms for high-order discretizations of parabolic problems
Alexandre Ern, Iain Smears, Martin Vohralik
We consider the a posteriori error analysis of fully discrete approximations of parabolic problems based on conforming -finite element methods in space and an arbitrary order d…
A Finite-Volume discretization of viscoelastic Saint-Venant equations for FENE-P fluids
Sébastien Boyaval
Saint-Venant equations can be generalized to account for a viscoelastic rheology in shallow flows. A Finite-Volume discretization for the 1D Saint-Venant system generalized to Uppe…
Stable broken and polynomial extensions for polynomial-degree-robust potential and flux reconstruction in three space dimensions
Alexandre Ern, Martin Vohralík
We study extensions of piecewise polynomial data prescribed on faces and possibly in elements of a patch of simplices sharing a vertex. In the setting, we look for functions…
Efficient spectral computation of the stationary states of rotating Bose-Einstein condensates by the preconditioned nonlinear conjugate gradient method
Xavier Antoine, Antoine Levitt, Qinglin Tang
We propose a preconditioned nonlinear conjugate gradient method coupled with a spectral spatial dis-cretization scheme for computing the ground states (GS) of rotating Bose-Einstei…
Discrete -robust -liftings and a posteriori estimates for elliptic problems with source terms
Alexandre Ern, Iain Smears, Martin Vohralík
We establish the existence of liftings into discrete subspaces of of piecewise polynomial data on locally refined simplicial partitions of polygonal/poly…
Variants of the Empirical Interpolation Method: symmetric formulation, choice of norms and rectangular extension
Fabien Casenave, Alexandre Ern, Tony Lelièvre
The Empirical Interpolation Method (EIM) is a greedy procedure that constructs approximate representations of two-variable functions in separated form. In its classical presentatio…
Accelerated dynamics: Mathematical foundations and algorithmic improvements
Tony Lelièvre
We present a review of recent works on the mathematical analysis of algorithms which have been proposed by A.F. Voter and co-workers in the late nineties in order to efficiently ge…
A nonintrusive Reduced Basis Method applied to aeroacoustic simulations
Fabien Casenave, Alexandre Ern, Tony Lelièvre
The Reduced Basis Method can be exploited in an efficient way only if the so-called affine dependence assumption on the operator and right-hand side of the considered problem with…
Efficiency of the Wang-Landau algorithm: a simple test case
G. Fort, B. Jourdain, E. Kuhn +2
We analyze the efficiency of the Wang-Landau algorithm to sample a multimodal distribution on a prototypical simple test case. We show that the exit time from a metastable state is…
Coupled BEM-FEM for the convected Helmholtz equation with non-uniform flow in a bounded domain
Fabien Casenave, Alexandre Ern, Guillaume Sylvand
We consider the convected Helmholtz equation modeling linear acoustic propagation at a fixed frequency in a subsonic flow around a scattering object. The flow is supposed to be uni…
Multi-Level Monte Carlo approaches for numerical homogenization
Yalchin Efendiev, Cornelia Kronsbein, Frederic Legoll
In this article, we study the application of Multi-Level Monte Carlo (MLMC) approaches to numerical random homogenization. Our objective is to compute the expectation of some funct…
Optimal non-reversible linear drift for the convergence to equilibrium of a diffusion
Tony Lelièvre, Francis Nier, Grigorios A. Pavliotis
We consider non-reversible perturbations of reversible diffusions that do not alter the invariant distribution and we ask whether there exists an optimal perturbation such that the…
Analysis of Compatible Discrete Operator Schemes for Elliptic Problems on Polyhedral Meshes
Jerome Bonelle, Alexandre Ern
Compatible schemes localize degrees of freedom according to the physical nature of the underlying fields and operate a clear distinction between topological laws and closure relati…
Epigraphical splitting for solving constrained convex formulations of inverse problems with proximal tools
Giovanni Chierchia, Nelly Pustelnik, Jean-Christophe Pesquet +1
We propose a proximal approach to deal with a class of convex variational problems involving nonlinear constraints. A large family of constraints, proven to be effective in the sol…
A new model for shallow viscoelastic fluids
François Bouchut, Sébastien Boyaval
We propose a new reduced model for gravity-driven free-surface flows of shallow elastic fluids. It is obtained by an asymptotic expansion of the upper-convected Maxwell model for e…