Alexandre Ern

Publication Activity (10 Years)

Years Active: 1994-2024
Publications (10 Years): 64

Top Venues

CoRR

SIAM J. Numer. Anal.

J. Sci. Comput.

Comput. Math. Appl.

Publications

Abbas Kabalan, Fabien Casenave, Felipe Bordeu, Virginie Ehrlacher, Alexandre Ern
An elasticity-based mesh morphing technique with application to reduced-order modeling. CoRR (2024)
Théophile Chaumont-Frelet, Alexandre Ern
Damped energy-norm a posteriori error estimates for fully discrete approximations of the wave equation using C2-reconstructions. CoRR (2024)
Alexandre Ern, Jean-Luc Guermond, Zuodong Wang
Asymptotic and Invariant-Domain Preserving Schemes for Scalar Conservation Equations with Stiff Source Terms and Multiple Equilibrium Points. J. Sci. Comput. 100 (3) (2024)
Alexandre Ern, Morgane Steins
Convergence Analysis for the Wave Equation Discretized with Hybrid Methods in Space (HHO, HDG and WG) and the Leapfrog Scheme in Time. J. Sci. Comput. 101 (1) (2024)
Alexandre Ern, Jean-Luc Guermond
The Discontinuous Galerkin Approximation of the Grad-Div and Curl-Curl Operators in First-Order Form Is Involution-Preserving and Spectrally Correct. SIAM J. Numer. Anal. 61 (6) (2023)
Alexandre Ern, Jean-Luc Guermond
Invariant-Domain Preserving High-Order Time Stepping: II. IMEX Schemes. SIAM J. Sci. Comput. 45 (5) (2023)
Erik Burman, Guillaume Delay, Alexandre Ern
The Unique Continuation Problem for the Heat Equation Discretized with a High-Order Space-Time Nonconforming Method. SIAM J. Numer. Anal. 61 (5) (2023)
Idrissa Niakh, Guillaume Drouet, Virginie Ehrlacher, Alexandre Ern
A reduced basis method for frictional contact problems formulated with Nitsche's method. CoRR (2023)
Théophile Chaumont-Frelet, Alexandre Ern
Asymptotic optimality of the edge finite element approximation of the time-harmonic Maxwell's equations. CoRR (2023)
Théophile Chaumont-Frelet, Alexandre Ern, Martin Vohralík
Stable broken H(curl) polynomial extensions and p-robust a posteriori error estimates by broken patchwise equilibration for the curl-curl problem. Math. Comput. 91 (333) (2022)
Alexandre Ern, Jean-Luc Guermond
Quasi-optimal Nonconforming Approximation of Elliptic PDEs with Contrasted Coefficients and $$H^{1+{r}}$$, $${r}>0$$, Regularity. Found. Comput. Math. 22 (5) (2022)
Zhaonan Dong, Alexandre Ern
-hybrid high-order methods for biharmonic problems. CoRR (2022)
Zhaonan Dong, Alexandre Ern
Hybrid High-Order and Weak Galerkin Methods for the Biharmonic Problem. SIAM J. Numer. Anal. 60 (5) (2022)
Alexandre Ern, Jean-Luc Guermond
Invariant-Domain-Preserving High-Order Time Stepping: I. Explicit Runge-Kutta Schemes. SIAM J. Sci. Comput. 44 (5) (2022)
Zhaonan Dong, Alexandre Ern, Jean-Luc Guermond
Local decay rates of best-approximation errors using vector-valued finite elements for fields with low regularity and integrable curl or divergence. CoRR (2022)
Riccardo Milani, Jérôme Bonelle, Alexandre Ern
Artificial Compressibility Methods for the Incompressible Navier-Stokes Equations Using Lowest-Order Face-Based Schemes on Polytopal Meshes. Comput. Methods Appl. Math. 22 (1) (2022)
Riccardo Milani, Jérôme Bonelle, Alexandre Ern
Artificial compressibility methods for the incompressible Navier-Stokes equations using lowest-order face-based schemes on polytopal meshes. CoRR (2021)
Zhaonan Dong, Alexandre Ern
Hybrid high-order method for singularly perturbed fourth-order problems on curved domains. CoRR (2021)
Matteo Cicuttin, Alexandre Ern, Nicolas Pignet
Hybrid high-order methods. A primer with application to solid mechanics. CoRR (2021)
Carsten Carstensen, Alexandre Ern, Sophie Puttkammer
Guaranteed lower bounds on eigenvalues of elliptic operators with a hybrid high-order method. Numerische Mathematik 149 (2) (2021)
Théophile Chaumont-Frelet, Alexandre Ern, Simon Lemaire, Frédéric Valentin
Bridging the Multiscale Hybrid-Mixed and Multiscale Hybrid High-Order methods. CoRR (2021)
Théophile Chaumont-Frelet, Alexandre Ern, Martin Vohralík
On the derivation of guaranteed and p-robust a posteriori error estimates for the Helmholtz equation. CoRR (2021)
Frédéric Marazzato, Alexandre Ern, Laurent Monasse
Quasi-static crack propagation with a Griffith criterion using a discrete element method. CoRR (2021)
Erik Burman, Omar Durán, Alexandre Ern, Morgane Steins
Convergence Analysis of Hybrid High-Order Methods for the Wave Equation. J. Sci. Comput. 87 (3) (2021)
Erik Burman, Matteo Cicuttin, Guillaume Delay, Alexandre Ern
An Unfitted Hybrid High-Order Method with Cell Agglomeration for Elliptic Interface Problems. SIAM J. Sci. Comput. 43 (2) (2021)
Théophile Chaumont-Frelet, Alexandre Ern, Martin Vohralík
On the derivation of guaranteed and p-robust a posteriori error estimates for the Helmholtz equation. Numerische Mathematik 148 (3) (2021)
Zhaonan Dong, Alexandre Ern
Hybrid high-order and weak Galerkin methods for the biharmonic problem. CoRR (2021)
Erik Burman, Guillaume Delay, Alexandre Ern
A Hybridized High-Order Method for Unique Continuation Subject to the Helmholtz Equation. SIAM J. Numer. Anal. 59 (5) (2021)
Fleurianne Bertrand, Alexandre Ern, Florin Adrian Radu
Robust and reliable finite element methods in poromechanics. Comput. Math. Appl. 91 (2021)
Quanling Deng, Alexandre Ern
SoftFEM: Revisiting the spectral finite element approximation of second-order elliptic operators. Comput. Math. Appl. 101 (2021)
Théophile Chaumont-Frelet, Alexandre Ern, Martin Vohralík
Polynomial-degree-robust H(curl)-stability of discrete minimization in a tetrahedron. CoRR (2020)
Théophile Chaumont-Frelet, Alexandre Ern, Martin Vohralík
Stable broken H(curl) polynomial extensions and p-robust quasi-equilibrated a posteriori estimators for Maxwell's equations. CoRR (2020)
Alexandre Ern, Martin Vohralík
and H(div) polynomial extensions for polynomial-degree-robust potential and flux reconstruction in three space dimensions. Math. Comput. 89 (322) (2020)
Matteo Cicuttin, Alexandre Ern, Thirupathi Gudi
Hybrid High-Order Methods for the Elliptic Obstacle Problem. J. Sci. Comput. 83 (1) (2020)
Frédéric Marazzato, Alexandre Ern, Christian Mariotti, Laurent Monasse
An explicit pseudo-energy conserving time-integration scheme for Hamiltonian dynamics. CoRR (2020)
Franz Chouly, Alexandre Ern, Nicolas Pignet
A Hybrid High-Order Discretization Combined with Nitsche's Method for Contact and Tresca Friction in Small Strain Elasticity. SIAM J. Sci. Comput. 42 (4) (2020)
Quanling Deng, Alexandre Ern
SoftFEM: revisiting the spectral finite element approximation of elliptic operators. CoRR (2020)
Victor M. Calo, Matteo Cicuttin, Quanling Deng, Alexandre Ern
Spectral approximation of elliptic operators by the Hybrid High-Order method. Math. Comput. 88 (318) (2019)
Alexandre Ern, Thirupathi Gudi, Iain Smears, Martin Vohralík
Equivalence of local-and global-best approximations, a simple stable local commuting projector, and optimal hp approximation estimates in H(div). CoRR (2019)
Tony Lelièvre, Simona Perotto, Gianluigi Rozza, Daniele A. Di Pietro, Alexandre Ern, Luca Formaggia
Preface: Special Issue on Model Reduction. J. Sci. Comput. 81 (1) (2019)
Florent Hédin, Géraldine Pichot, Alexandre Ern
A Hybrid High-Order Method for Flow Simulations in Discrete Fracture Networks. ENUMATH (2019)
Mickaël Abbas, Alexandre Ern, Nicolas Pignet
A Hybrid High-Order method for finite elastoplastic deformations within a logarithmic strain framework. CoRR (2019)
Frédéric Marazzato, Alexandre Ern, Laurent Monasse
A consistent discrete element method for quasi-static and dynamic elasto-plasticity. CoRR (2019)
Erik Burman, Guillaume Delay, Alexandre Ern
The Unfitted HHO Method for the Stokes Problem on Curved Domains. ENUMATH (2019)
Victor M. Calo, Alexandre Ern, Ignacio Muga, Sergio Rojas
An adaptive stabilized finite element method based on residual minimization. CoRR (2019)
Matteo Cicuttin, Alexandre Ern, Simon Lemaire
A Hybrid High-Order Method for Highly Oscillatory Elliptic Problems. Comput. Methods Appl. Math. 19 (4) (2019)
Alexandre Ern, Jean-Luc Guermond
Abstract Nonconforming Error Estimates and Application to Boundary Penalty Methods for Diffusion Equations and Time-Harmonic Maxwell's Equations. Comput. Methods Appl. Math. 18 (3) (2018)
Karol L. Cascavita, Jérémy Bleyer, Xavier Chateau, Alexandre Ern
Hybrid Discretization Methods with Adaptive Yield Surface Detection for Bingham Pipe Flows. J. Sci. Comput. 77 (3) (2018)
Amina Benaceur, Virginie Ehrlacher, Alexandre Ern, Sébastien Meunier
A Progressive Reduced Basis/Empirical Interpolation Method for Nonlinear Parabolic Problems. SIAM J. Sci. Comput. 40 (5) (2018)
Matteo Cicuttin, Daniele A. Di Pietro, Alexandre Ern
Implementation of Discontinuous Skeletal methods on arbitrary-dimensional, polytopal meshes using generic programming. J. Comput. Appl. Math. 344 (2018)
Erik Burman, Alexandre Ern
An Unfitted Hybrid High-Order Method for Elliptic Interface Problems. SIAM J. Numer. Anal. 56 (3) (2018)
Mickaël Abbas, Alexandre Ern, Nicolas Pignet
A Hybrid High-Order method for incremental associative plasticity with small deformations. CoRR (2018)
Patrik Daniel, Alexandre Ern, Iain Smears, Martin Vohralík
An adaptive hp-refinement strategy with computable guaranteed bound on the error reduction factor. Comput. Math. Appl. 76 (5) (2018)
Alexandre Ern, Jean-Luc Guermond
Analysis of the edge finite element approximation of the Maxwell equations with low regularity solutions. Comput. Math. Appl. 75 (3) (2018)
Christelle Lusso, Alexandre Ern, François Bouchut, Anne Mangeney, Maxime Farin, Olivier Roche
Two-dimensional simulation by regularization of free surface viscoplastic flows with Drucker-Prager yield stress and application to granular collapse. J. Comput. Phys. 333 (2017)
Mickaël Abbas, Alexandre Ern, Nicolas Pignet
Hybrid High-Order methods for finite deformations of hyperelastic materials. CoRR (2017)
Rita Riedlbeck, Daniele A. Di Pietro, Alexandre Ern, Sylvie Granet, Kyrylo Kazymyrenko
Stress and flux reconstruction in Biot's poro-elasticity problem with application to a posteriori error analysis. Comput. Math. Appl. 73 (7) (2017)
Alexandre Ern, Iain Smears, Martin Vohralík
Guaranteed, Locally Space-Time Efficient, and Polynomial-Degree Robust a Posteriori Error Estimates for High-Order Discretizations of Parabolic Problems. SIAM J. Numer. Anal. 55 (6) (2017)
Alexandre Ern, Friedhelm Schieweck
Discontinuous Galerkin method in time combined with a stabilized finite element method in space for linear first-order PDEs. Math. Comput. 85 (301) (2016)
Pierre Cantin, Alexandre Ern
Vertex-Based Compatible Discrete Operator Schemes on Polyhedral Meshes for Advection-Diffusion Equations. Comput. Methods Appl. Math. 16 (2) (2016)
Pierre Cantin, Jérôme Bonelle, Erik Burman, Alexandre Ern
A vertex-based scheme on polyhedral meshes for advection-reaction equations with sub-mesh stabilization. Comput. Math. Appl. 72 (9) (2016)
Alexandre Ern, Jean-Luc Guermond
Mollification in Strongly Lipschitz Domains with Application to Continuous and Discrete De Rham Complexes. Comput. Methods Appl. Math. 16 (1) (2016)
Fabien Casenave, Alexandre Ern, Tony Lelièvre
Variants of the Empirical Interpolation Method: Symmetric formulation, choice of norms and rectangular extension. Appl. Math. Lett. 56 (2016)
Vít Dolejsí, Alexandre Ern, Martin Vohralík
hp-Adaptation Driven by Polynomial-Degree-Robust A Posteriori Error Estimates for Elliptic Problems. SIAM J. Sci. Comput. 38 (5) (2016)
Maria Adela Puscas, Laurent Monasse, Alexandre Ern, Christian Tenaud, Christian Mariotti, Virginie Daru
A time semi-implicit scheme for the energy-balanced coupling of a shocked fluid flow with a deformable structure. J. Comput. Phys. 296 (2015)
Fabien Casenave, Alexandre Ern, Tony Lelièvre
A nonintrusive reduced basis method applied to aeroacoustic simulations. Adv. Comput. Math. 41 (5) (2015)
Lorenzo Contento, Alexandre Ern, Rossana Vermiglio
A linear-time approximate convex envelope algorithm using the double Legendre-Fenchel transform with application to phase separation. Comput. Optim. Appl. 60 (1) (2015)
Daniele A. Di Pietro, Jérôme Droniou, Alexandre Ern
A Discontinuous-Skeletal Method for Advection-Diffusion-Reaction on General Meshes. SIAM J. Numer. Anal. 53 (5) (2015)
Alexandre Ern, Martin Vohralík
Polynomial-Degree-Robust A Posteriori Estimates in a Unified Setting for Conforming, Nonconforming, Discontinuous Galerkin, and Mixed Discretizations. SIAM J. Numer. Anal. 53 (2) (2015)
Jérôme Bonelle, Daniele A. Di Pietro, Alexandre Ern
Low-order reconstruction operators on polyhedral meshes: application to compatible discrete operator schemes. Comput. Aided Geom. Des. (2015)
Fabien Casenave, Alexandre Ern, Guillaume Sylvand
Coupled BEM-FEM for the convected Helmholtz equation with non-uniform flow in a bounded domain. J. Comput. Phys. 257 (2014)
Daniele A. Di Pietro, Alexandre Ern, Simon Lemaire
An Arbitrary-Order and Compact-Stencil Discretization of Diffusion on General Meshes Based on Local Reconstruction Operators. Comput. Methods Appl. Math. 14 (4) (2014)
Jerome Bonelle, Alexandre Ern
Analysis of Compatible Discrete Operator Schemes for the Stokes Equations on Polyhedral Meshes. CoRR (2014)
Vít Dolejsí, Alexandre Ern, Martin Vohralík
A Framework for Robust A Posteriori Error Control in Unsteady Nonlinear Advection-Diffusion Problems. SIAM J. Numer. Anal. 51 (2) (2013)
Alexandre Ern, Martin Vohralík
Adaptive Inexact Newton Methods with A Posteriori Stopping Criteria for Nonlinear Diffusion PDEs. SIAM J. Sci. Comput. 35 (4) (2013)
Alexandre Ern, Jean-Luc Guermond
Weighting the Edge Stabilization. SIAM J. Numer. Anal. 51 (3) (2013)
J. Tryoen, Olivier P. Le Maître, Alexandre Ern
Adaptive Anisotropic Spectral Stochastic Methods for Uncertain Scalar Conservation Laws. SIAM J. Sci. Comput. 34 (5) (2012)
David Doyen, Alexandre Ern
Analysis of the Modified Mass Method for the Dynamic Signorini Problem with Coulomb Friction. SIAM J. Numer. Anal. 49 (5) (2011)
David Doyen, Alexandre Ern, Serge Piperno
Time-Integration Schemes for the Finite Element Dynamic Signorini Problem. SIAM J. Sci. Comput. 33 (1) (2011)
J. Tryoen, Olivier P. Le Maître, Michael Ndjinga, Alexandre Ern
Roe solver with entropy corrector for uncertain hyperbolic systems. J. Comput. Appl. Math. 235 (2) (2010)
Erik Burman, Alexandre Ern, Miguel A. Fernández
Explicit Runge-Kutta Schemes and Finite Elements with Symmetric Stabilization for First-Order Linear PDE Systems. SIAM J. Numer. Anal. 48 (6) (2010)
J. Tryoen, Olivier P. Le Maître, Michael Ndjinga, Alexandre Ern
Intrusive Galerkin methods with upwinding for uncertain nonlinear hyperbolic systems. J. Comput. Phys. 229 (18) (2010)
Alexandre Ern, Annette F. Stephansen, Martin Vohralík
Guaranteed and robust discontinuous Galerkin a posteriori error estimates for convection-diffusion-reaction problems. J. Comput. Appl. Math. 234 (1) (2010)
Daniele A. Di Pietro, Alexandre Ern
Discrete functional analysis tools for Discontinuous Galerkin methods with application to the incompressible Navier-Stokes equations. Math. Comput. 79 (271) (2010)
Alexandre Ern, Martin Vohralík
A Posteriori Error Estimation Based on Potential and Flux Reconstruction for the Heat Equation. SIAM J. Numer. Anal. 48 (1) (2010)
Simona Perotto, Alexandre Ern, Alessandro Veneziani
Hierarchical Local Model Reduction for Elliptic Problems: A Domain Decomposition Approach. Multiscale Model. Simul. 8 (4) (2010)
Boujemâa Achchab, M. El Fatini, Alexandre Ern, Ali Souissi
A posteriori error estimates for subgrid viscosity stabilized approximations of convection-diffusion equations. Appl. Math. Lett. 22 (9) (2009)
Anne Bourlioux, Alexandre Ern, Pascal Turbis
A Posteriori Error Estimation for Subgrid Flamelet Models. Multiscale Model. Simul. 8 (2) (2009)
Daniele A. Di Pietro, Alexandre Ern, Jean-Luc Guermond
Discontinuous Galerkin Methods for Anisotropic Semidefinite Diffusion with Advection. SIAM J. Numer. Anal. 46 (2) (2008)
Alexandre Ern, Jean-Luc Guermond
Discontinuous Galerkin Methods for Friedrichs' Systems. Part III. Multifield Theories with Partial Coercivity. SIAM J. Numer. Anal. 46 (2) (2008)
Erik Burman, Alexandre Ern
-finite element methods for advection and advection-diffusion equations. Math. Comput. 76 (259) (2007)
Alexandre Ern, Jean-Luc Guermond
Discontinuous Galerkin Methods for Friedrichs' Systems. Part II. Second-order Elliptic PDEs. SIAM J. Numer. Anal. 44 (6) (2006)
Alexandre Ern, Jean-Luc Guermond
Discontinuous Galerkin Methods for Friedrichs' Systems. I. General theory. SIAM J. Numer. Anal. 44 (2) (2006)
Erik Burman, Alexandre Ern
Stabilized Galerkin approximation of convection-diffusion-reaction equations: discrete maximum principle and convergence. Math. Comput. 74 (252) (2005)
Alexandre Ern, Jennifer Proft
A posteriori discontinuous Galerkin error estimates for transient convection-diffusion equations. Appl. Math. Lett. 18 (7) (2005)
Jean-Pierre Croisille, Alexandre Ern, Tony Lelièvre, Jennifer Proft
Analysis and simulation of a coupled hyperbolic/parabolic model problem. J. Num. Math. 13 (2) (2005)
Malte Braack, Alexandre Ern
A Posteriori Control of Modeling Errors and Discretization Errors. Multiscale Model. Simul. 1 (2) (2003)
Craig C. Douglas, Alexandre Ern, Mitchell D. Smooke
Multigrid Solution of Flame Sheet Problems on Serial and Parallel Computers. Parallel Algorithms Appl. 10 (3-4) (1997)
Alexandre Ern, Craig C. Douglas, Mitchell D. Smooke
Detailed Chemistry Modeling of Laminar Diffusion Flames On Parallel Computers. Int. J. High Perform. Comput. Appl. 9 (3) (1995)
Alexandre Ern, Vincent Giovangigli, David E. Keyes, Mitchell D. Smooke
Towards Polyalgorithmic Linear System Solvers for Nonlinear Elliptic Problems. SIAM J. Sci. Comput. 15 (3) (1994)

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Publication Activity (10 Years)

Top Topics

Top Venues

Alexandre Ern