Alexandre Ern

According to our database1, Alexandre Ern authored at least 94 papers between 1994 and 2023.

Collaborative distances:
  • Dijkstra number2 of four.
  • Erdős number3 of four.

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Bibliography

2023
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., December, 2023

Invariant-Domain Preserving High-Order Time Stepping: II. IMEX Schemes.
SIAM J. Sci. Comput., October, 2023

The Unique Continuation Problem for the Heat Equation Discretized with a High-Order Space-Time Nonconforming Method.
SIAM J. Numer. Anal., October, 2023

Asymptotic optimality of the edge finite element approximation of the time-harmonic Maxwell's equations.
CoRR, 2023

A reduced basis method for frictional contact problems formulated with Nitsche's method.
CoRR, 2023

2022
Invariant-Domain-Preserving High-Order Time Stepping: I. Explicit Runge-Kutta Schemes.
SIAM J. Sci. Comput., October, 2022

Hybrid High-Order and Weak Galerkin Methods for the Biharmonic Problem.
SIAM J. Numer. Anal., 2022

Stable broken H(curl) polynomial extensions and p-robust a posteriori error estimates by broken patchwise equilibration for the curl-curl problem.
Math. Comput., 2022

Quasi-optimal Nonconforming Approximation of Elliptic PDEs with Contrasted Coefficients and $$H^{1+{r}}$$, $${r}>0$$, Regularity.
Found. Comput. Math., 2022

C<sup>0</sup>-hybrid high-order methods for biharmonic problems.
CoRR, 2022

Local decay rates of best-approximation errors using vector-valued finite elements for fields with low regularity and integrable curl or divergence.
CoRR, 2022

Artificial Compressibility Methods for the Incompressible Navier-Stokes Equations Using Lowest-Order Face-Based Schemes on Polytopal Meshes.
Comput. Methods Appl. Math., 2022

2021
An Unfitted Hybrid High-Order Method with Cell Agglomeration for Elliptic Interface Problems.
SIAM J. Sci. Comput., 2021

A Hybridized High-Order Method for Unique Continuation Subject to the Helmholtz Equation.
SIAM J. Numer. Anal., 2021

On the derivation of guaranteed and p-robust a posteriori error estimates for the Helmholtz equation.
Numerische Mathematik, 2021

Guaranteed lower bounds on eigenvalues of elliptic operators with a hybrid high-order method.
Numerische Mathematik, 2021

Convergence Analysis of Hybrid High-Order Methods for the Wave Equation.
J. Sci. Comput., 2021

Hybrid high-order method for singularly perturbed fourth-order problems on curved domains.
CoRR, 2021

Hybrid high-order methods. A primer with application to solid mechanics.
CoRR, 2021

Bridging the Multiscale Hybrid-Mixed and Multiscale Hybrid High-Order methods.
CoRR, 2021

Quasi-static crack propagation with a Griffith criterion using a discrete element method.
CoRR, 2021

SoftFEM: Revisiting the spectral finite element approximation of second-order elliptic operators.
Comput. Math. Appl., 2021

Robust and reliable finite element methods in poromechanics.
Comput. Math. Appl., 2021

2020
A Hybrid High-Order Discretization Combined with Nitsche's Method for Contact and Tresca Friction in Small Strain Elasticity.
SIAM J. Sci. Comput., 2020

Stable broken H<sup>1</sup> and H(div) polynomial extensions for polynomial-degree-robust potential and flux reconstruction in three space dimensions.
Math. Comput., 2020

Hybrid High-Order Methods for the Elliptic Obstacle Problem.
J. Sci. Comput., 2020

SoftFEM: revisiting the spectral finite element approximation of elliptic operators.
CoRR, 2020

An explicit pseudo-energy conserving time-integration scheme for Hamiltonian dynamics.
CoRR, 2020

Stable broken H(curl) polynomial extensions and p-robust quasi-equilibrated a posteriori estimators for Maxwell's equations.
CoRR, 2020

Polynomial-degree-robust H(curl)-stability of discrete minimization in a tetrahedron.
CoRR, 2020

2019
Spectral approximation of elliptic operators by the Hybrid High-Order method.
Math. Comput., 2019

Preface: Special Issue on Model Reduction.
J. Sci. Comput., 2019

A consistent discrete element method for quasi-static and dynamic elasto-plasticity.
CoRR, 2019

Equivalence of local-and global-best approximations, a simple stable local commuting projector, and optimal hp approximation estimates in H(div).
CoRR, 2019

An adaptive stabilized finite element method based on residual minimization.
CoRR, 2019

A Hybrid High-Order method for finite elastoplastic deformations within a logarithmic strain framework.
CoRR, 2019

A Hybrid High-Order Method for Highly Oscillatory Elliptic Problems.
Comput. Methods Appl. Math., 2019

A Hybrid High-Order Method for Flow Simulations in Discrete Fracture Networks.
Proceedings of the Numerical Mathematics and Advanced Applications ENUMATH 2019 - European Conference, Egmond aan Zee, The Netherlands, September 30, 2019

The Unfitted HHO Method for the Stokes Problem on Curved Domains.
Proceedings of the Numerical Mathematics and Advanced Applications ENUMATH 2019 - European Conference, Egmond aan Zee, The Netherlands, September 30, 2019

2018
A Progressive Reduced Basis/Empirical Interpolation Method for Nonlinear Parabolic Problems.
SIAM J. Sci. Comput., 2018

An Unfitted Hybrid High-Order Method for Elliptic Interface Problems.
SIAM J. Numer. Anal., 2018

Hybrid Discretization Methods with Adaptive Yield Surface Detection for Bingham Pipe Flows.
J. Sci. Comput., 2018

Implementation of Discontinuous Skeletal methods on arbitrary-dimensional, polytopal meshes using generic programming.
J. Comput. Appl. Math., 2018

A Hybrid High-Order method for incremental associative plasticity with small deformations.
CoRR, 2018

Abstract Nonconforming Error Estimates and Application to Boundary Penalty Methods for Diffusion Equations and Time-Harmonic Maxwell's Equations.
Comput. Methods Appl. Math., 2018

Analysis of the edge finite element approximation of the Maxwell equations with low regularity solutions.
Comput. Math. Appl., 2018

An adaptive hp-refinement strategy with computable guaranteed bound on the error reduction factor.
Comput. Math. Appl., 2018

2017
Guaranteed, Locally Space-Time Efficient, and Polynomial-Degree Robust a Posteriori Error Estimates for High-Order Discretizations of Parabolic Problems.
SIAM J. Numer. Anal., 2017

Two-dimensional simulation by regularization of free surface viscoplastic flows with Drucker-Prager yield stress and application to granular collapse.
J. Comput. Phys., 2017

Hybrid High-Order methods for finite deformations of hyperelastic materials.
CoRR, 2017

Stress and flux reconstruction in Biot's poro-elasticity problem with application to a posteriori error analysis.
Comput. Math. Appl., 2017

2016
hp-Adaptation Driven by Polynomial-Degree-Robust A Posteriori Error Estimates for Elliptic Problems.
SIAM J. Sci. Comput., 2016

Discontinuous Galerkin method in time combined with a stabilized finite element method in space for linear first-order PDEs.
Math. Comput., 2016

Mollification in Strongly Lipschitz Domains with Application to Continuous and Discrete De Rham Complexes.
Comput. Methods Appl. Math., 2016

Vertex-Based Compatible Discrete Operator Schemes on Polyhedral Meshes for Advection-Diffusion Equations.
Comput. Methods Appl. Math., 2016

A vertex-based scheme on polyhedral meshes for advection-reaction equations with sub-mesh stabilization.
Comput. Math. Appl., 2016

Variants of the Empirical Interpolation Method: Symmetric formulation, choice of norms and rectangular extension.
Appl. Math. Lett., 2016

2015
A Discontinuous-Skeletal Method for Advection-Diffusion-Reaction on General Meshes.
SIAM J. Numer. Anal., 2015

Polynomial-Degree-Robust A Posteriori Estimates in a Unified Setting for Conforming, Nonconforming, Discontinuous Galerkin, and Mixed Discretizations.
SIAM J. Numer. Anal., 2015

A time semi-implicit scheme for the energy-balanced coupling of a shocked fluid flow with a deformable structure.
J. Comput. Phys., 2015

A linear-time approximate convex envelope algorithm using the double Legendre-Fenchel transform with application to phase separation.
Comput. Optim. Appl., 2015

Low-order reconstruction operators on polyhedral meshes: application to compatible discrete operator schemes.
Comput. Aided Geom. Des., 2015

A nonintrusive reduced basis method applied to aeroacoustic simulations.
Adv. Comput. Math., 2015

2014
Coupled BEM-FEM for the convected Helmholtz equation with non-uniform flow in a bounded domain.
J. Comput. Phys., 2014

Analysis of Compatible Discrete Operator Schemes for the Stokes Equations on Polyhedral Meshes.
CoRR, 2014

An Arbitrary-Order and Compact-Stencil Discretization of Diffusion on General Meshes Based on Local Reconstruction Operators.
Comput. Methods Appl. Math., 2014

2013
Adaptive Inexact Newton Methods with A Posteriori Stopping Criteria for Nonlinear Diffusion PDEs.
SIAM J. Sci. Comput., 2013

Weighting the Edge Stabilization.
SIAM J. Numer. Anal., 2013

A Framework for Robust A Posteriori Error Control in Unsteady Nonlinear Advection-Diffusion Problems.
SIAM J. Numer. Anal., 2013

2012
Adaptive Anisotropic Spectral Stochastic Methods for Uncertain Scalar Conservation Laws.
SIAM J. Sci. Comput., 2012

2011
Time-Integration Schemes for the Finite Element Dynamic Signorini Problem.
SIAM J. Sci. Comput., 2011

Analysis of the Modified Mass Method for the Dynamic Signorini Problem with Coulomb Friction.
SIAM J. Numer. Anal., 2011

2010
A Posteriori Error Estimation Based on Potential and Flux Reconstruction for the Heat Equation.
SIAM J. Numer. Anal., 2010

Explicit Runge-Kutta Schemes and Finite Elements with Symmetric Stabilization for First-Order Linear PDE Systems.
SIAM J. Numer. Anal., 2010

Discrete functional analysis tools for Discontinuous Galerkin methods with application to the incompressible Navier-Stokes equations.
Math. Comput., 2010

Hierarchical Local Model Reduction for Elliptic Problems: A Domain Decomposition Approach.
Multiscale Model. Simul., 2010

Intrusive Galerkin methods with upwinding for uncertain nonlinear hyperbolic systems.
J. Comput. Phys., 2010

Roe solver with entropy corrector for uncertain hyperbolic systems.
J. Comput. Appl. Math., 2010

Guaranteed and robust discontinuous Galerkin a posteriori error estimates for convection-diffusion-reaction problems.
J. Comput. Appl. Math., 2010

2009
A Posteriori Error Estimation for Subgrid Flamelet Models.
Multiscale Model. Simul., 2009

A posteriori error estimates for subgrid viscosity stabilized approximations of convection-diffusion equations.
Appl. Math. Lett., 2009

2008
Discontinuous Galerkin Methods for Anisotropic Semidefinite Diffusion with Advection.
SIAM J. Numer. Anal., 2008

Discontinuous Galerkin Methods for Friedrichs' Systems. Part III. Multifield Theories with Partial Coercivity.
SIAM J. Numer. Anal., 2008

2007
Continuous interior penalty <i>hp</i>-finite element methods for advection and advection-diffusion equations.
Math. Comput., 2007

2006
Discontinuous Galerkin Methods for Friedrichs' Systems. Part II. Second-order Elliptic PDEs.
SIAM J. Numer. Anal., 2006

Discontinuous Galerkin Methods for Friedrichs' Systems. I. General theory.
SIAM J. Numer. Anal., 2006

2005
Stabilized Galerkin approximation of convection-diffusion-reaction equations: discrete maximum principle and convergence.
Math. Comput., 2005

Analysis and simulation of a coupled hyperbolic/parabolic model problem.
J. Num. Math., 2005

A posteriori discontinuous Galerkin error estimates for transient convection-diffusion equations.
Appl. Math. Lett., 2005

2003
A Posteriori Control of Modeling Errors and Discretization Errors.
Multiscale Model. Simul., 2003

1997
Multigrid Solution of Flame Sheet Problems on Serial and Parallel Computers.
Parallel Algorithms Appl., 1997

1996
Numerical Simulation of Laminar Diffusion Flames.
Proceedings of the Applications on Advanced Architecture Computers, 1996

1995
Detailed Chemistry Modeling of Laminar Diffusion Flames On Parallel Computers.
Int. J. High Perform. Comput. Appl., 1995

1994
Towards Polyalgorithmic Linear System Solvers for Nonlinear Elliptic Problems.
SIAM J. Sci. Comput., 1994


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