Towards Polyalgorithmic Linear System Solvers for Nonlinear Elliptic Problems. - Alexandre Ern; Vincent Giovangigli; David E. Keyes; Mitchell D. Smooke (SIAM J. Sci. Comput., 1994)

Detailed Chemistry Modeling of Laminar Diffusion Flames On Parallel Computers. - Alexandre Ern; Craig C. Douglas; Mitchell D. Smooke (Int. J. High Perform. Comput. Appl., 1995)

Numerical Simulation of Laminar Diffusion Flames. - Craig C. Douglas; Alexandre Ern; Mitchell D. Smooke (Applications on Advanced Architecture Computers, 1996)

Multigrid Solution of Flame Sheet Problems on Serial and Parallel Computers. - Craig C. Douglas; Alexandre Ern; Mitchell D. Smooke (Parallel Algorithms Appl., 1997)

A Posteriori Control of Modeling Errors and Discretization Errors. - Malte Braack; Alexandre Ern (Multiscale Model. Simul., 2003)

A posteriori discontinuous Galerkin error estimates for transient convection-diffusion equations. - Alexandre Ern; Jennifer Proft (Appl. Math. Lett., 2005)

Analysis and simulation of a coupled hyperbolic/parabolic model problem. - Jean-Pierre Croisille; Alexandre Ern; Tony Lelièvre; Jennifer Proft (J. Num. Math., 2005)

Stabilized Galerkin approximation of convection-diffusion-reaction equations: discrete maximum principle and convergence. - Erik Burman; Alexandre Ern (Math. Comput., 2005)

Discontinuous Galerkin Methods for Friedrichs' Systems. I. General theory. - Alexandre Ern; Jean-Luc Guermond (SIAM J. Numer. Anal., 2006)

Discontinuous Galerkin Methods for Friedrichs' Systems. Part II. Second-order Elliptic PDEs. - Alexandre Ern; Jean-Luc Guermond (SIAM J. Numer. Anal., 2006)

Continuous interior penalty hp-finite element methods for advection and advection-diffusion equations. - Erik Burman; Alexandre Ern (Math. Comput., 2007)

Discontinuous Galerkin Methods for Friedrichs' Systems. Part III. Multifield Theories with Partial Coercivity. - Alexandre Ern; Jean-Luc Guermond (SIAM J. Numer. Anal., 2008)

Discontinuous Galerkin Methods for Anisotropic Semidefinite Diffusion with Advection. - Daniele A. Di Pietro; Alexandre Ern; Jean-Luc Guermond (SIAM J. Numer. Anal., 2008)

A posteriori error estimates for subgrid viscosity stabilized approximations of convection-diffusion equations. - Boujemâa Achchab; Mohamed El Fatini; Alexandre Ern; Ali Souissi (Appl. Math. Lett., 2009)

A Posteriori Error Estimation for Subgrid Flamelet Models. - Anne Bourlioux; Alexandre Ern; Pascal Turbis (Multiscale Model. Simul., 2009)

Guaranteed and robust discontinuous Galerkin a posteriori error estimates for convection-diffusion-reaction problems. - Alexandre Ern; Annette F. Stephansen; Martin Vohralík (J. Comput. Appl. Math., 2010)

Roe solver with entropy corrector for uncertain hyperbolic systems. - J. Tryoen; Olivier P. Le Maître; Michael Ndjinga; Alexandre Ern (J. Comput. Appl. Math., 2010)

Intrusive Galerkin methods with upwinding for uncertain nonlinear hyperbolic systems. - J. Tryoen; Olivier P. Le Maître; Michael Ndjinga; Alexandre Ern (J. Comput. Phys., 2010)

Hierarchical Local Model Reduction for Elliptic Problems: A Domain Decomposition Approach. - Simona Perotto; Alexandre Ern; Alessandro Veneziani (Multiscale Model. Simul., 2010)

Discrete functional analysis tools for Discontinuous Galerkin methods with application to the incompressible Navier-Stokes equations. - Daniele A. Di Pietro; Alexandre Ern (Math. Comput., 2010)

Explicit Runge-Kutta Schemes and Finite Elements with Symmetric Stabilization for First-Order Linear PDE Systems. - Erik Burman; Alexandre Ern; Miguel A. Fernández (SIAM J. Numer. Anal., 2010)

A Posteriori Error Estimation Based on Potential and Flux Reconstruction for the Heat Equation. - Alexandre Ern; Martin Vohralík (SIAM J. Numer. Anal., 2010)

Analysis of the Modified Mass Method for the Dynamic Signorini Problem with Coulomb Friction. - David Doyen; Alexandre Ern (SIAM J. Numer. Anal., 2011)

Time-Integration Schemes for the Finite Element Dynamic Signorini Problem. - David Doyen; Alexandre Ern; Serge Piperno (SIAM J. Sci. Comput., 2011)

Adaptive Anisotropic Spectral Stochastic Methods for Uncertain Scalar Conservation Laws. - J. Tryoen; Olivier P. Le Maître; Alexandre Ern (SIAM J. Sci. Comput., 2012)

A Framework for Robust A Posteriori Error Control in Unsteady Nonlinear Advection-Diffusion Problems. - Vít Dolejsí; Alexandre Ern; Martin Vohralík (SIAM J. Numer. Anal., 2013)

Weighting the Edge Stabilization. - Alexandre Ern; Jean-Luc Guermond (SIAM J. Numer. Anal., 2013)

Adaptive Inexact Newton Methods with A Posteriori Stopping Criteria for Nonlinear Diffusion PDEs. - Alexandre Ern; Martin Vohralík (SIAM J. Sci. Comput., 2013)

An Arbitrary-Order and Compact-Stencil Discretization of Diffusion on General Meshes Based on Local Reconstruction Operators. - Daniele A. Di Pietro; Alexandre Ern; Simon Lemaire (Comput. Methods Appl. Math., 2014)

Analysis of Compatible Discrete Operator Schemes for the Stokes Equations on Polyhedral Meshes. - Jerome Bonelle; Alexandre Ern (CoRR, 2014)

Coupled BEM-FEM for the convected Helmholtz equation with non-uniform flow in a bounded domain. - Fabien Casenave; Alexandre Ern; Guillaume Sylvand (J. Comput. Phys., 2014)

A nonintrusive reduced basis method applied to aeroacoustic simulations. - Fabien Casenave; Alexandre Ern; Tony Lelièvre (Adv. Comput. Math., 2015)

Low-order reconstruction operators on polyhedral meshes: application to compatible discrete operator schemes. - Jérôme Bonelle; Daniele A. Di Pietro; Alexandre Ern (Comput. Aided Geom. Des., 2015)

A linear-time approximate convex envelope algorithm using the double Legendre-Fenchel transform with application to phase separation. - Lorenzo Contento; Alexandre Ern; Rossana Vermiglio (Comput. Optim. Appl., 2015)

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; Virginie Daru (J. Comput. Phys., 2015)

Polynomial-Degree-Robust A Posteriori Estimates in a Unified Setting for Conforming, Nonconforming, Discontinuous Galerkin, and Mixed Discretizations. - Alexandre Ern; Martin Vohralík (SIAM J. Numer. Anal., 2015)

A Discontinuous-Skeletal Method for Advection-Diffusion-Reaction on General Meshes. - Daniele A. Di Pietro; Jérôme Droniou; Alexandre Ern (SIAM J. Numer. Anal., 2015)

Variants of the Empirical Interpolation Method: Symmetric formulation, choice of norms and rectangular extension. - Fabien Casenave; Alexandre Ern; Tony Lelièvre (Appl. Math. Lett., 2016)

A vertex-based scheme on polyhedral meshes for advection-reaction equations with sub-mesh stabilization. - Pierre Cantin; Jérôme Bonelle; Erik Burman; Alexandre Ern (Comput. Math. Appl., 2016)

Vertex-Based Compatible Discrete Operator Schemes on Polyhedral Meshes for Advection-Diffusion Equations. - Pierre Cantin; Alexandre Ern (Comput. Methods Appl. Math., 2016)

Mollification in Strongly Lipschitz Domains with Application to Continuous and Discrete De Rham Complexes. - Alexandre Ern; Jean-Luc Guermond (Comput. Methods Appl. Math., 2016)

Discontinuous Galerkin method in time combined with a stabilized finite element method in space for linear first-order PDEs. - Alexandre Ern; Friedhelm Schieweck (Math. Comput., 2016)

hp-Adaptation Driven by Polynomial-Degree-Robust A Posteriori Error Estimates for Elliptic Problems. - Vít Dolejsí; Alexandre Ern; Martin Vohralík (SIAM J. Sci. Comput., 2016)

Stress and flux reconstruction in Biot's poro-elasticity problem with application to a posteriori error analysis. - Rita Riedlbeck; Daniele A. Di Pietro; Alexandre Ern; Sylvie Granet; Kyrylo Kazymyrenko (Comput. Math. Appl., 2017)

Hybrid High-Order methods for finite deformations of hyperelastic materials. - Mickaël Abbas; Alexandre Ern; Nicolas Pignet (CoRR, 2017)

Two-dimensional simulation by regularization of free surface viscoplastic flows with Drucker-Prager yield stress and application to granular collapse. - Christelle Lusso; Alexandre Ern; François Bouchut; Anne Mangeney; Maxime Farin; Olivier Roche (J. Comput. Phys., 2017)

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 J. Numer. Anal., 2017)

An adaptive hp-refinement strategy with computable guaranteed bound on the error reduction factor. - Patrik Daniel; Alexandre Ern; Iain Smears; Martin Vohralík (Comput. Math. Appl., 2018)

Analysis of the edge finite element approximation of the Maxwell equations with low regularity solutions. - Alexandre Ern; Jean-Luc Guermond (Comput. Math. Appl., 2018)

Abstract Nonconforming Error Estimates and Application to Boundary Penalty Methods for Diffusion Equations and Time-Harmonic Maxwell's Equations. - Alexandre Ern; Jean-Luc Guermond (Comput. Methods Appl. Math., 2018)

A Hybrid High-Order method for incremental associative plasticity with small deformations. - Mickaël Abbas; Alexandre Ern; Nicolas Pignet (CoRR, 2018)

Implementation of Discontinuous Skeletal methods on arbitrary-dimensional, polytopal meshes using generic programming. - Matteo Cicuttin; Daniele A. Di Pietro; Alexandre Ern (J. Comput. Appl. Math., 2018)

Hybrid Discretization Methods with Adaptive Yield Surface Detection for Bingham Pipe Flows. - Karol L. Cascavita; Jérémy Bleyer; Xavier Chateau; Alexandre Ern (J. Sci. Comput., 2018)

An Unfitted Hybrid High-Order Method for Elliptic Interface Problems. - Erik Burman; Alexandre Ern (SIAM J. Numer. Anal., 2018)

A Progressive Reduced Basis/Empirical Interpolation Method for Nonlinear Parabolic Problems. - Amina Benaceur; Virginie Ehrlacher; Alexandre Ern; Sébastien Meunier (SIAM J. Sci. Comput., 2018)

The Unfitted HHO Method for the Stokes Problem on Curved Domains. - Erik Burman; Guillaume Delay; Alexandre Ern (ENUMATH, 2019)

A Hybrid High-Order Method for Flow Simulations in Discrete Fracture Networks. - Florent Hédin; Géraldine Pichot; Alexandre Ern (ENUMATH, 2019)

A Hybrid High-Order Method for Highly Oscillatory Elliptic Problems. - Matteo Cicuttin; Alexandre Ern; Simon Lemaire (Comput. Methods Appl. Math., 2019)

A Hybrid High-Order method for finite elastoplastic deformations within a logarithmic strain framework. - Mickaël Abbas; Alexandre Ern; Nicolas Pignet (CoRR, 2019)

An adaptive stabilized finite element method based on residual minimization. - Victor M. Calo; Alexandre Ern; Ignacio Muga; Sergio Rojas (CoRR, 2019)

Equivalence of local-and global-best approximations, a simple stable local commuting projector, and optimal hp approximation estimates in H(div). - Alexandre Ern; Thirupathi Gudi; Iain Smears; Martin Vohralík (CoRR, 2019)

A consistent discrete element method for quasi-static and dynamic elasto-plasticity. - Frédéric Marazzato; Alexandre Ern; Laurent Monasse (CoRR, 2019)

Preface: Special Issue on Model Reduction. - Tony Lelièvre; Simona Perotto; Gianluigi Rozza; Daniele A. Di Pietro; Alexandre Ern; Luca Formaggia (J. Sci. Comput., 2019)

Spectral approximation of elliptic operators by the Hybrid High-Order method. - Victor M. Calo; Matteo Cicuttin; Quanling Deng; Alexandre Ern (Math. Comput., 2019)

Polynomial-degree-robust H(curl)-stability of discrete minimization in a tetrahedron. - Théophile Chaumont-Frelet; Alexandre Ern; Martin Vohralík (CoRR, 2020)

Stable broken H(curl) polynomial extensions and p-robust quasi-equilibrated a posteriori estimators for Maxwell's equations. - Théophile Chaumont-Frelet; Alexandre Ern; Martin Vohralík (CoRR, 2020)

An explicit pseudo-energy conserving time-integration scheme for Hamiltonian dynamics. - Frédéric Marazzato; Alexandre Ern; Christian Mariotti; Laurent Monasse (CoRR, 2020)

SoftFEM: revisiting the spectral finite element approximation of elliptic operators. - Quanling Deng; Alexandre Ern (CoRR, 2020)

Hybrid High-Order Methods for the Elliptic Obstacle Problem. - Matteo Cicuttin; Alexandre Ern; Thirupathi Gudi (J. Sci. Comput., 2020)

Stable broken H1 and H(div) polynomial extensions for polynomial-degree-robust potential and flux reconstruction in three space dimensions. - Alexandre Ern; Martin Vohralík (Math. Comput., 2020)

A Hybrid High-Order Discretization Combined with Nitsche's Method for Contact and Tresca Friction in Small Strain Elasticity. - Franz Chouly; Alexandre Ern; Nicolas Pignet (SIAM J. Sci. Comput., 2020)

Robust and reliable finite element methods in poromechanics. - Fleurianne Bertrand; Alexandre Ern; Florin Adrian Radu (Comput. Math. Appl., 2021)

SoftFEM: Revisiting the spectral finite element approximation of second-order elliptic operators. - Quanling Deng; Alexandre Ern (Comput. Math. Appl., 2021)

Quasi-static crack propagation with a Griffith criterion using a discrete element method. - Frédéric Marazzato; Alexandre Ern; Laurent Monasse (CoRR, 2021)

Bridging the Multiscale Hybrid-Mixed and Multiscale Hybrid High-Order methods. - Théophile Chaumont-Frelet; Alexandre Ern; Simon Lemaire; Frédéric Valentin (CoRR, 2021)

Hybrid high-order methods. A primer with application to solid mechanics. - Matteo Cicuttin; Alexandre Ern; Nicolas Pignet (CoRR, 2021)

Hybrid high-order method for singularly perturbed fourth-order problems on curved domains. - Zhaonan Dong; Alexandre Ern (CoRR, 2021)

Convergence Analysis of Hybrid High-Order Methods for the Wave Equation. - Erik Burman; Omar Durán; Alexandre Ern; Morgane Steins (J. Sci. Comput., 2021)

Guaranteed lower bounds on eigenvalues of elliptic operators with a hybrid high-order method. - Carsten Carstensen; Alexandre Ern; Sophie Puttkammer (Numerische Mathematik, 2021)

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)

A Hybridized High-Order Method for Unique Continuation Subject to the Helmholtz Equation. - Erik Burman; Guillaume Delay; Alexandre Ern (SIAM J. Numer. Anal., 2021)

An Unfitted Hybrid High-Order Method with Cell Agglomeration for Elliptic Interface Problems. - Erik Burman; Matteo Cicuttin; Guillaume Delay; Alexandre Ern (SIAM J. Sci. Comput., 2021)

Artificial Compressibility Methods for the Incompressible Navier-Stokes Equations Using Lowest-Order Face-Based Schemes on Polytopal Meshes. - Riccardo Milani; Jérôme Bonelle; Alexandre Ern (Comput. Methods Appl. Math., 2022)

Local decay rates of best-approximation errors using vector-valued finite elements for fields with low regularity and integrable curl or divergence. - Zhaonan Dong; Alexandre Ern; Jean-Luc Guermond (CoRR, 2022)

C0-hybrid high-order methods for biharmonic problems. - Zhaonan Dong; Alexandre Ern (CoRR, 2022)

Quasi-optimal Nonconforming Approximation of Elliptic PDEs with Contrasted Coefficients and $$H^{1+{r}}$$, $${r}>0$$, Regularity. - Alexandre Ern; Jean-Luc Guermond (Found. Comput. Math., 2022)

Stable broken H(curl) polynomial extensions and p-robust a posteriori error estimates by broken patchwise equilibration for the curl-curl problem. - Théophile Chaumont-Frelet; Alexandre Ern; Martin Vohralík (Math. Comput., 2022)

Hybrid High-Order and Weak Galerkin Methods for the Biharmonic Problem. - Zhaonan Dong; Alexandre Ern (SIAM J. Numer. Anal., 2022)

Invariant-Domain-Preserving High-Order Time Stepping: I. Explicit Runge-Kutta Schemes. - Alexandre Ern; Jean-Luc Guermond (SIAM J. Sci. Comput., 2022)

A reduced basis method for frictional contact problems formulated with Nitsche's method. - Idrissa Niakh; Guillaume Drouet; Virginie Ehrlacher; Alexandre Ern (CoRR, 2023)

Asymptotic optimality of the edge finite element approximation of the time-harmonic Maxwell's equations. - Théophile Chaumont-Frelet; Alexandre Ern (CoRR, 2023)

The Unique Continuation Problem for the Heat Equation Discretized with a High-Order Space-Time Nonconforming Method. - Erik Burman; Guillaume Delay; Alexandre Ern (SIAM J. Numer. Anal., 2023)

Invariant-Domain Preserving High-Order Time Stepping: II. IMEX Schemes. - Alexandre Ern; Jean-Luc Guermond (SIAM J. Sci. Comput., 2023)

The Discontinuous Galerkin Approximation of the Grad-Div and Curl-Curl Operators in First-Order Form Is Involution-Preserving and Spectrally Correct. - Alexandre Ern; Jean-Luc Guermond (SIAM J. Numer. Anal., 2023)

Damped energy-norm a posteriori error estimates for fully discrete approximations of the wave equation using C2-reconstructions. - Théophile Chaumont-Frelet; Alexandre Ern (CoRR, 2024)

An elasticity-based mesh morphing technique with application to reduced-order modeling. - Abbas Kabalan; Fabien Casenave; Felipe Bordeu; Virginie Ehrlacher; Alexandre Ern (CoRR, 2024)

hp-error analysis of mixed-order hybrid high-order methods for elliptic problems on simplicial meshes. - Zhaonan Dong; Alexandre Ern (CoRR, 2024)

Discrete Poincaré inequalities: a review on proofs, equivalent formulations, and behavior of constants. - Alexandre Ern; Johnny Guzmán; Pratyush Potu; Martin Vohralík (CoRR, 2024)

A priori and a posteriori analysis of the discontinuous Galerkin approximation of the time-harmonic Maxwell's equations under minimal regularity assumptions. - Théophile Chaumont-Frelet; Alexandre Ern (CoRR, 2024)

Asymptotic and Invariant-Domain Preserving Schemes for Scalar Conservation Equations with Stiff Source Terms and Multiple Equilibrium Points. - Alexandre Ern; Jean-Luc Guermond; Zuodong Wang (J. Sci. Comput., 2024)

Convergence Analysis for the Wave Equation Discretized with Hybrid Methods in Space (HHO, HDG and WG) and the Leapfrog Scheme in Time. - Alexandre Ern; Morgane Steins (J. Sci. Comput., 2024)

Spectral Correctness of the Simplicial Discontinuous Galerkin Approximation of the First-Order Form of Maxwell's Equations with Discontinuous Coefficients. - Alexandre Ern; Jean-Luc Guermond (SIAM J. Numer. Anal., 2025)

Third-Order Sectorially A-Stable Alternating Implicit Runge-Kutta Schemes. - Alexandre Ern; Jean-Luc Guermond (SIAM J. Sci. Comput., 2025)

Local L2-bounded commuting projections using discrete local problems on Alfeld splits. - Alexandre Ern; Johnny Guzmán; Pratyush Potu; Martin Vohralík (CoRR, 2025)

Hybrid high-order methods for elasto-acoustic wave propagation in the time domain. - Romain Mottier; Alexandre Ern; Rekha Khot; Laurent Guillot (CoRR, 2025)

Unfitted hybrid high-order methods stabilized by polynomial extension for elliptic interface problems. - Erik Burman; Alexandre Ern; Romain Mottier (CoRR, 2025)

Elasto-acoustic wave propagation in geophysical media using hybrid high-order methods on general meshes. - Romain Mottier; Alexandre Ern; Laurent Guillot (CoRR, 2025)

Hcurl-reconstruction of piecewise polynomial fields with application to hp-a posteriori nonconforming error analysis for Maxwell's equations. - Zhaonan Dong; Alexandre Ern (CoRR, 2025)