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Finite Elements III: First-Order and Time-Dependent PDEs

Alexandre Ern , Jean-Luc Guermond
Books hal-03226051v1
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Implementation of Discontinuous Skeletal methods on arbitrary-dimensional, polytopal meshes using generic programming

Matteo Cicuttin , Daniele Di Pietro , Alexandre Ern
Journal of Computational and Applied Mathematics, 2018, 344 (15), pp.852-874. ⟨10.1016/⟩
Journal articles hal-01429292v3
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Stable model reduction for linear variational inequalities with parameter-dependent constraints

Idrissa Niakh , Guillaume Drouet , Virginie Ehrlacher , Alexandre Ern
Preprints, Working Papers, ... hal-03611982v3
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Efficient Solvers based on Hybrid High-Order (HHO) methods for flow simulations in fractured rocks

Alexandre Ern , Florent Hédin , Géraldine Pichot , Nicolas Pignet
Journée contrat-cadre Inria-IFPEN, Nov 2021, Rueil-Malmaison, France
Conference papers hal-03538747v1
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A vertex-based scheme on polyhedral meshes for advection-reaction equations with sub-mesh stabilization

Pierre Cantin , Jérôme Bonelle , Erik Burman , Alexandre Ern
Computers & Mathematics with Applications, 2016, ⟨10.1016/j.camwa.2016.07.038⟩
Journal articles hal-01285957v2
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Adaptive inexact Newton methods with a posteriori stopping criteria for nonlinear diffusion PDEs

Alexandre Ern , Martin Vohralík
SIAM Journal on Scientific Computing, 2013, 35 (4), pp.A1761-A1791. ⟨10.1137/120896918⟩
Journal articles hal-00681422v2
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The unique continuation problem for the heat equation discretized with a high-order space-time nonconforming method

Erik Burman , Guillaume Delay , Alexandre Ern
Preprints, Working Papers, ... hal-03720960v3

Coupled BEM-FEM for the convected Helmholtz equation with non-uniform flow in a bounded domain

Fabien Casenave , Alexandre Ern , Guillaume Sylvand
Journal of Computational Physics, 2014, 257 (A), pp.627-644. ⟨10.1016/⟩
Journal articles hal-00805477v1
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Phase separation in highly charged confined ionic solutions

Rémi Joubaud , Olivier Bernard , Lorenzo Contento , Alexandre Ern , Benjamin Rotenberg , et al.
Preprints, Working Papers, ... hal-00806218v1
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A three-field augmented Lagrangian formulation of unilateral contact problems with cohesive forces

David Doyen , Alexandre Ern , Serge Piperno
ESAIM: Mathematical Modelling and Numerical Analysis, 2010, 44 (2), pp.323-346. ⟨10.1051/m2an/2010004⟩
Journal articles hal-00349836v1
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Adaptive Anisotropic Spectral Stochastic Methods for Uncertain Scalar Conservation Laws

Julie Tryoen , Olivier Le Maitre , Alexandre Ern
Reports hal-00681200v1
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Arbitrary-order mixed methods for heterogeneous anisotropic diffusion on general meshes

Daniele Antonio Di Pietro , Alexandre Ern
IMA Journal of Numerical Analysis, 2017, 37 (1), pp.40-63. ⟨10.1093/imanum/drw003⟩
Journal articles hal-00918482v3
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Analysis of the modified mass method for the dynamic Signorini problem with Coulomb friction

David Doyen , Alexandre Ern
SIAM Journal on Numerical Analysis, 2011, 49 (5), pp.2039-2056. ⟨10.1137/100804711⟩
Journal articles hal-00473809v1
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Bridging the Hybrid High-Order and Hybridizable Discontinuous Galerkin Methods

Bernardo Cockburn , Daniele Di Pietro , Alexandre Ern
ESAIM: Mathematical Modelling and Numerical Analysis, 2016, Polyhedral discretization for PDE, 50 (3), pp.635-650. ⟨10.1051/m2an/2015051⟩
Journal articles hal-01115318v2
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Fractional-step methods and finite elements with symmetric stabilization for the transient Oseen problem

Erik Burman , Alexandre Ern , Miguel Angel Fernández
ESAIM: Mathematical Modelling and Numerical Analysis, 2017, 51 (2), pp.487-507. ⟨10.1051/m2an/2016028⟩
Journal articles hal-01218328v1
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Compatible Discrete Operator schemes for the steady incompressible Stokes and Navier-Stokes equations

Riccardo Milani , Jérôme Bonelle , Alexandre Ern
FVCA - Finite Volumes for Complex Applications IX, Jun 2020, Bergen, Norway
Conference papers hal-02417514v2

A Discontinuous Skeletal Method for Bingham Fluids

Karol L Cascavita , Jeremy Bleyer , Xavier Chateau , Alexandre Ern
13th World Congress on Computational Mechanics (WCCM XIII), Jul 2018, New York, United States
Conference papers hal-02434344v1
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Discontinuous Galerkin method in time combined with a stabilized finite element method in space for linear first-order PDEs

Alexandre Ern , Friedhelm Schieweck
Mathematics of Computation, 2016, 85 (301), pp.2099-2129. ⟨10.1090/mcom/3073⟩
Journal articles hal-00947695v2
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Stable broken H1 and H(div) polynomial extensions for polynomial-degree-robust potential and flux reconstruction in three space dimensions

Alexandre Ern , Martin Vohralík
Mathematics of Computation, 2020, 89 (322), pp.551-594. ⟨10.1090/mcom/3482⟩
Journal articles hal-01422204v4
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An unfitted Hybrid High-Order method with cell agglomeration for elliptic interface problems

Erik Burman , Matteo Cicuttin , Guillaume Delay , Alexandre Ern
SIAM Journal on Scientific Computing, 2021, 43 (2), pp.A859-A882. ⟨10.1137/19M1285901⟩
Journal articles hal-02280426v5
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Polynomial-degree-robust a posteriori error estimation for Maxwell's equations

Théophile Chaumont-Frelet , Alexandre Ern , Martin Vohralík
WCCM & ECCOMAS Congress 2020 - 14th World Congress in Computational Mechanics and ECCOMAS Congress, Jan 2021, Paris, France
Conference papers hal-03403840v1
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Bridging the Multiscale Hybrid-Mixed and Multiscale Hybrid High-Order methods

Théophile Chaumont-Frelet , Alexandre Ern , Simon Lemaire , Frédéric Valentin
ESAIM: Mathematical Modelling and Numerical Analysis, 2022, 56 (1), pp.261-285. ⟨10.1051/m2an/2021082⟩
Journal articles hal-03235525v3
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Finite Elements II: Galerkin Approximation, Elliptic and Mixed PDEs

Alexandre Ern , Jean-Luc Guermond
Books hal-03226050v1
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A linear-time approximate convex envelope algorithm using the double Legendre--Fenchel transform with application to phase separation

Lorenzo Contento , Alexandre Ern , Rossana Vermiglio
Computational Optimization and Applications, 2015, ⟨10.1007/s10589-014-9666-8⟩
Journal articles hal-00806597v2
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An adaptive stabilized conforming finite element method via residual minimization on dual discontinuous Galerkin norms

Victor M Calo , Alexandre Ern , Ignacio Muga , Sergio Rojas
Computer Methods in Applied Mechanics and Engineering, 2020, ⟨10.1016/j.cma.2020.112891⟩
Journal articles hal-02196242v3

A nonintrusive reduced basis method applied to aeroacoustic simulations

Fabien Casenave , Alexandre Ern , Tony Lelièvre
Advances in Computational Mathematics, 2014, 41 (5), pp.961 - 986. ⟨10.1007/s10444-014-9365-0⟩
Journal articles hal-00934641v1
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Equilibrated tractions for the Hybrid High-Order method

Daniele Di Pietro , Alexandre Ern
Comptes Rendus. Mathématique, 2015, 353 (3), pp.279--282. ⟨10.1016/j.crma.2014.12.009⟩
Journal articles hal-01079026v2
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Numerical study of a thin liquid film flowing down an inclined wavy plane

Alexandre Ern , Rémi Joubaud , Tony Lelièvre
Physica D: Nonlinear Phenomena, 2011, 240 (21), pp.1714-1723. ⟨10.1016/j.physd.2011.07.007⟩
Journal articles hal-00533000v2
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A time semi-implicit scheme for the energy-balanced coupling of a shocked fluid flow with a deformable structure

Maria Adela Puscas , Laurent Monasse , Alexandre Ern , Christian Tenaud , Christian Mariotti , et al.
Journal of Computational Physics, 2015, 296, pp.241-262. ⟨10.1016/⟩
Journal articles hal-00993324v3
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A discontinuous skeletal method for the viscosity-dependent Stokes problem

Daniele Di Pietro , Alexandre Ern , Alexander Linke , Friedhelm Schieweck
Computer Methods in Applied Mechanics and Engineering, 2016, 306, pp.175-195. ⟨10.1016/j.cma.2016.03.033⟩
Journal articles hal-01244387v2