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authIdHal_s : alexandre-ern
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Implicit-Explicit Runge-Kutta schemes and finite elements with symmetric stabilization for advection-diffusion equations

Erik Burman , Alexandre Ern
2010
Preprints, Working Papers, ... hal-00530378v1
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A double-layer Boussinesq-type model for highly nonlinear and dispersive waves

Florent Chazel , Michel Benoit , Alexandre Ern , Serge Piperno
2009
Preprints, Working Papers, ... hal-00371036v1
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Explicit Runge--Kutta schemes and finite elements with symmetric stabilization for first-order linear PDE systems

Erik Burman , Alexandre Ern , Miguel Angel Fernández
SIAM Journal on Numerical Analysis, 2010, 48 (6), pp.2019-2042. ⟨10.1137/090757940⟩
Journal articles hal-00380659v1
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A posteriori error estimation based on potential and flux reconstruction for the heat equation

Alexandre Ern , Martin Vohralík
SIAM Journal on Numerical Analysis, 2010, 48 (1), pp.198-223. ⟨10.1137/090759008⟩
Journal articles hal-00383692v1
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A posteriori error analysis of Euler-Galerkin approximations to coupled elliptic-parabolic problems

Alexandre Ern , Sébastien Meunier
ESAIM: Mathematical Modelling and Numerical Analysis, 2007, pp.1
Journal articles hal-00164851v1
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A posteriori energy-norm error estimates for advection-diffusion equations approximated by weighted interior penalty methods

Alexandre Ern , Annette Stephansen
2007
Preprints, Working Papers, ... hal-00171838v1
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Une nouvelle méthode de relaxation pour les équations de Navier-Stokes compressibles. II : validation numérique

Emmanuel Bongiovanni , Alexandre Ern , Nathalie Glinsky-Olivier
RR-4605, INRIA. 2002
Reports inria-00071980v1
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An unfitted Hybrid High-Order method for elliptic interface problems

Erik Burman , Alexandre Ern
SIAM Journal on Numerical Analysis, 2018, 56 (3), pp.1525-1546
Journal articles hal-01625421v2
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Low-rank approximation of linear parabolic equations by space-time tensor Galerkin methods

Thomas Boiveau , Virginie Ehrlacher , Alexandre Ern , Anthony Nouy
ESAIM: Mathematical Modelling and Numerical Analysis, 2019, 53 (2), pp.635-658. ⟨10.1051/m2an/2018073⟩
Journal articles hal-01668316v2
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An adaptive $hp$-refinement strategy with computable guaranteed bound on the error reduction factor

Patrik Daniel , Alexandre Ern , Iain Smears , Martin Vohralík
Computers & Mathematics with Applications, 2018, 76 (5), pp.967-983. ⟨10.1016/j.camwa.2018.05.034⟩
Journal articles hal-01666763v2
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Discrete $p$-robust H(div)-liftings and a posteriori estimates for elliptic problems with $H^{-1}$ source terms

Alexandre Ern , Iain Smears , Martin Vohralík
Calcolo, 2017, 54 (3), pp.1009-1025. ⟨10.1007/s10092-017-0217-4⟩
Journal articles hal-01377007v1

Discontinuous Galerkin Methods for Anisotropic Semidefinite Diffusion with Advection

Daniele Antonio Di Pietro , Alexandre Ern , Jean-Luc Guermond
SIAM Journal on Numerical Analysis, 2008, 46 (2), pp.805 - 831. ⟨10.1137/060676106⟩
Journal articles hal-01818201v1

A nonintrusive method to approximate linear systems with nonlinear parameter dependence

Fabien Casenave , Alexandre Ern , Tony Lelièvre , Guillaume Sylvand
2013
Preprints, Working Papers, ... hal-00845822v1
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A framework for robust a posteriori error control in unsteady nonlinear advection-diffusion problems

Vít Dolejší , Alexandre Ern , Martin Vohralík
SIAM Journal on Numerical Analysis, 2013, 51 (2), pp.773-793. ⟨10.1137/110859282⟩
Journal articles hal-00652979v2
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Polynomial-degree-robust a posteriori error estimation for Maxwell's equations

Théophile Chaumont-Frelet , Alexandre Ern , Martin Vohralík
ICOSAHOM 2021 - International Conference on Spectral High Order Methods, Jul 2021, Vienna, Austria
Conference papers hal-03403944v1
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Quasi-static crack propagation with a Griffith criterion using a variational discrete element method

Frédéric Marazzato , Alexandre Ern , Laurent Monasse
2021
Preprints, Working Papers, ... hal-03102982v3
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Low-order reconstruction operators on polyhedral meshes: application to compatible discrete operator schemes

Jerome Bonelle , Daniele Di Pietro , Alexandre Ern
Computer Aided Geometric Design, 2015, 35-36, pp.27-41. ⟨10.1016/j.cagd.2015.03.015⟩
Journal articles hal-01097311v1
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Analysis of Compatible Discrete Operator Schemes for Elliptic Problems on Polyhedral Meshes

Jérôme Bonelle , Alexandre Ern
ESAIM: Mathematical Modelling and Numerical Analysis, 2014, 48 (02), pp.553--581. ⟨10.1051/m2an/2013104⟩
Journal articles hal-00751284v2

The symmetric discontinuous Galerkin method does not need stabilization in 1D for polynomial orders

Erik Burman , Alexandre Ern , Igor Mozolevski , Benjamin Stamm
Comptes rendus de l'Académie des sciences. Série I, Mathématique, 2007, 345 (10), pp.599--602. ⟨10.1016/j.crma.2007.10.028⟩
Journal articles hal-01090911v1
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Numerical study of density functional theory with mean spherical approximation for ionic condensation in highly charged confined electrolytes

Rémi Joubaud , Olivier Bernard , Alfred Delville , Alexandre Ern , Benjamin Rotenberg , et al.
Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, 2014, 89, pp.062302. ⟨10.1103/PhysRevE.89.062302⟩
Journal articles hal-00992323v1
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A quasi-optimal variant of the hybrid high-order method for elliptic PDEs with $H^{ −1}$ loads

Alexandre Ern , Pietro Zanotti
IMA Journal of Numerical Analysis, 2020, 40 (4), ⟨10.1093/imanum/drz057⟩
Journal articles hal-02114715v1
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On the derivation of guaranteed and p-robust a posteriori error estimates for the Helmholtz equation

Théophile Chaumont-Frelet , Alexandre Ern , Martin Vohralík
Numerische Mathematik, 2021, 148 (3), pp.525-573. ⟨10.1007/s00211-021-01192-w⟩
Journal articles hal-02202233v3
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Asymptotically constant-free, p-robust and guaranteed a posteriori error estimates for the Helmholtz equation

Théophile Chaumont-Frelet , Alexandre Ern , Martin Vohralík
EnuMath 2019 - European Numerical Mathematics and Advanced Applications Conference, Sep 2019, Egmond aan Zee, Netherlands
Conference papers hal-02321140v1
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Guaranteed error estimates for finite element discretizations of Helmholtz problems

Théophile Chaumont-Frelet , Alexandre Ern , Martin Vohralík
Numerical Waves, Oct 2021, Nice, France
Conference papers hal-03404014v1
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Analysis of a discontinuous Galerkin method for heterogeneous diffusion problems with low-regularity solutions

Daniele Antonio Di Pietro , Alexandre Ern
Numerical Methods for Partial Differential Equations, 2011, 17 p. ⟨10.1002/num.20675⟩
Journal articles hal-00514387v1
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Intrusive projection methods with upwinding for uncertain nonlinear hyperbolic systems

Julie Tryoen , Olivier Le Maitre , Michael Ndjinga , Alexandre Ern
Journal of Computational Physics, 2010, 229 (18), pp.6485-6511. ⟨10.1016/j.jcp.2010.05.007⟩
Journal articles hal-00375616v2
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Abstract nonconforming error estimates and application to boundary penalty methods for diffusion equations and time-harmonic Maxwell's equations

Alexandre Ern , Jean-Luc Guermond
Computational Methods in Applied Mathematics, 2018, 18 (3), pp.451-475. ⟨10.1515/cmam-2017-0058⟩
Journal articles hal-01563594v4
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Guaranteed, locally space-time efficient, and polynomial-degree robust a posteriori error estimates for high-order discretizations of parabolic problems

Alexandre Ern , Iain Smears , Martin Vohralík
SIAM Journal on Numerical Analysis, 2017, 55 (6), pp.2811-2834. ⟨10.1137/16M1097626⟩
Journal articles hal-01377086v1
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A hybridized high-order method for unique continuation subject to the Helmholtz equation

Erik Burman , Guillaume Delay , Alexandre Ern
SIAM Journal on Numerical Analysis, 2021, 59 (5), pp.2368-2392
Journal articles hal-02977024v3

Variants of the Empirical Interpolation Method: Symmetric formulation, choice of norms and rectangular extension

Fabien Casenave , Alexandre Ern , Tony Lelièvre
Applied Mathematics Letters, 2016, 56, pp.23 - 28. ⟨10.1016/j.aml.2015.11.010⟩
Journal articles hal-01186039v1