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Alexandre Ern
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2020 – today
- 2024
- [j74]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): 83 (2024) - [j73]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): 7 (2024) - [i24]Théophile Chaumont-Frelet, Alexandre Ern:
Damped energy-norm a posteriori error estimates for fully discrete approximations of the wave equation using C2-reconstructions. CoRR abs/2403.12954 (2024) - [i23]Abbas Kabalan, Fabien Casenave, Felipe Bordeu, Virginie Ehrlacher, Alexandre Ern:
An elasticity-based mesh morphing technique with application to reduced-order modeling. CoRR abs/2407.02433 (2024) - 2023
- [j72]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): 2534-2557 (2023) - [j71]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): 2940-2966 (2023) - [j70]Alexandre Ern, Jean-Luc Guermond
:
Invariant-Domain Preserving High-Order Time Stepping: II. IMEX Schemes. SIAM J. Sci. Comput. 45(5): 2511- (2023) - [i22]Idrissa Niakh, Guillaume Drouet, Virginie Ehrlacher, Alexandre Ern:
A reduced basis method for frictional contact problems formulated with Nitsche's method. CoRR abs/2307.11541 (2023) - [i21]Théophile Chaumont-Frelet, Alexandre Ern:
Asymptotic optimality of the edge finite element approximation of the time-harmonic Maxwell's equations. CoRR abs/2309.14189 (2023) - 2022
- [j69]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): 133-154 (2022) - [j68]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): 1273-1308 (2022) - [j67]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): 37-74 (2022) - [j66]Zhaonan Dong
, Alexandre Ern:
Hybrid High-Order and Weak Galerkin Methods for the Biharmonic Problem. SIAM J. Numer. Anal. 60(5): 2626-2656 (2022) - [j65]Alexandre Ern, Jean-Luc Guermond
:
Invariant-Domain-Preserving High-Order Time Stepping: I. Explicit Runge-Kutta Schemes. SIAM J. Sci. Comput. 44(5): 3366- (2022) - [i20]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 abs/2201.01708 (2022) - [i19]Zhaonan Dong, Alexandre Ern:
C0-hybrid high-order methods for biharmonic problems. CoRR abs/2206.07074 (2022) - 2021
- [j64]Fleurianne Bertrand
, Alexandre Ern, Florin Adrian Radu
:
Robust and reliable finite element methods in poromechanics. Comput. Math. Appl. 91: 1-2 (2021) - [j63]Quanling Deng
, Alexandre Ern:
SoftFEM: Revisiting the spectral finite element approximation of second-order elliptic operators. Comput. Math. Appl. 101: 119-133 (2021) - [j62]Erik Burman, Omar Durán
, Alexandre Ern, Morgane Steins:
Convergence Analysis of Hybrid High-Order Methods for the Wave Equation. J. Sci. Comput. 87(3): 91 (2021) - [j61]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): 525-573 (2021) - [j60]Carsten Carstensen, Alexandre Ern, Sophie Puttkammer:
Guaranteed lower bounds on eigenvalues of elliptic operators with a hybrid high-order method. Numerische Mathematik 149(2): 273-304 (2021) - [j59]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): 2368-2392 (2021) - [j58]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): A859-A882 (2021) - [i18]Frédéric Marazzato, Alexandre Ern, Laurent Monasse:
Quasi-static crack propagation with a Griffith criterion using a discrete element method. CoRR abs/2101.02763 (2021) - [i17]Zhaonan Dong, Alexandre Ern:
Hybrid high-order and weak Galerkin methods for the biharmonic problem. CoRR abs/2103.16404 (2021) - [i16]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 abs/2105.00914 (2021) - [i15]Théophile Chaumont-Frelet
, Alexandre Ern, Martin Vohralík:
On the derivation of guaranteed and p-robust a posteriori error estimates for the Helmholtz equation. CoRR abs/2105.01376 (2021) - [i14]Théophile Chaumont-Frelet, Alexandre Ern, Simon Lemaire, Frédéric Valentin:
Bridging the Multiscale Hybrid-Mixed and Multiscale Hybrid High-Order methods. CoRR abs/2106.01693 (2021) - [i13]Matteo Cicuttin
, Alexandre Ern, Nicolas Pignet:
Hybrid high-order methods. A primer with application to solid mechanics. CoRR abs/2106.09348 (2021) - [i12]Zhaonan Dong, Alexandre Ern:
Hybrid high-order method for singularly perturbed fourth-order problems on curved domains. CoRR abs/2108.08348 (2021) - 2020
- [j57]Matteo Cicuttin
, Alexandre Ern, Thirupathi Gudi:
Hybrid High-Order Methods for the Elliptic Obstacle Problem. J. Sci. Comput. 83(1): 8 (2020) - [j56]Alexandre Ern, Martin Vohralík
:
Stable broken H1 and H(div) polynomial extensions for polynomial-degree-robust potential and flux reconstruction in three space dimensions. Math. Comput. 89(322): 551-594 (2020) - [j55]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): A2300-A2324 (2020) - [i11]Théophile Chaumont-Frelet
, Alexandre Ern, Martin Vohralík:
Polynomial-degree-robust H(curl)-stability of discrete minimization in a tetrahedron. CoRR abs/2005.14528 (2020) - [i10]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 abs/2005.14537 (2020) - [i9]Frédéric Marazzato, Alexandre Ern, Christian Mariotti, Laurent Monasse:
An explicit pseudo-energy conserving time-integration scheme for Hamiltonian dynamics. CoRR abs/2008.06000 (2020) - [i8]Quanling Deng, Alexandre Ern:
SoftFEM: revisiting the spectral finite element approximation of elliptic operators. CoRR abs/2011.06953 (2020)
2010 – 2019
- 2019
- [j54]Matteo Cicuttin
, Alexandre Ern, Simon Lemaire:
A Hybrid High-Order Method for Highly Oscillatory Elliptic Problems. Comput. Methods Appl. Math. 19(4): 723-748 (2019) - [j53]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): 1-2 (2019) - [j52]Victor M. Calo, Matteo Cicuttin
, Quanling Deng
, Alexandre Ern:
Spectral approximation of elliptic operators by the Hybrid High-Order method. Math. Comput. 88(318): 1559-1586 (2019) - [c2]Erik Burman, Guillaume Delay, Alexandre Ern:
The Unfitted HHO Method for the Stokes Problem on Curved Domains. ENUMATH 2019: 389-397 - [c1]Florent Hédin
, Géraldine Pichot, Alexandre Ern:
A Hybrid High-Order Method for Flow Simulations in Discrete Fracture Networks. ENUMATH 2019: 521-529 - [i7]Mickaël Abbas, Alexandre Ern, Nicolas Pignet:
A Hybrid High-Order method for finite elastoplastic deformations within a logarithmic strain framework. CoRR abs/1901.04480 (2019) - [i6]Victor M. Calo, Alexandre Ern, Ignacio Muga, Sergio Rojas
:
An adaptive stabilized finite element method based on residual minimization. CoRR abs/1907.12605 (2019) - [i5]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 abs/1908.08158 (2019) - [i4]Frédéric Marazzato, Alexandre Ern, Laurent Monasse:
A consistent discrete element method for quasi-static and dynamic elasto-plasticity. CoRR abs/1911.00738 (2019) - 2018
- [j51]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): 918-932 (2018) - [j50]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): 967-983 (2018) - [j49]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): 451-475 (2018) - [j48]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: 852-874 (2018) - [j47]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): 1424-1443 (2018) - [j46]Erik Burman, Alexandre Ern:
An Unfitted Hybrid High-Order Method for Elliptic Interface Problems. SIAM J. Numer. Anal. 56(3): 1525-1546 (2018) - [j45]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): A2930-A2955 (2018) - [i3]Mickaël Abbas, Alexandre Ern, Nicolas Pignet:
A Hybrid High-Order method for incremental associative plasticity with small deformations. CoRR abs/1804.06129 (2018) - 2017
- [j44]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): 1593-1610 (2017) - [j43]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: 387-408 (2017) - [j42]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): 2811-2834 (2017) - [i2]Mickaël Abbas, Alexandre Ern, Nicolas Pignet:
Hybrid High-Order methods for finite deformations of hyperelastic materials. CoRR abs/1709.03747 (2017) - 2016
- [j41]Fabien Casenave
, Alexandre Ern, Tony Lelièvre
:
Variants of the Empirical Interpolation Method: Symmetric formulation, choice of norms and rectangular extension. Appl. Math. Lett. 56: 23-28 (2016) - [j40]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): 2057-2071 (2016) - [j39]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): 51-75 (2016) - [j38]Pierre Cantin, Alexandre Ern:
Vertex-Based Compatible Discrete Operator Schemes on Polyhedral Meshes for Advection-Diffusion Equations. Comput. Methods Appl. Math. 16(2): 187-212 (2016) - [j37]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): 2099-2129 (2016) - [j36]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) - 2015
- [j35]Fabien Casenave
, Alexandre Ern, Tony Lelièvre
:
A nonintrusive reduced basis method applied to aeroacoustic simulations. Adv. Comput. Math. 41(5): 961-986 (2015) - [j34]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. 35-36: 27-41 (2015) - [j33]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): 231-261 (2015) - [j32]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: 241-262 (2015) - [j31]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): 1058-1081 (2015) - [j30]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): 2135-2157 (2015) - 2014
- [j29]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): 461-472 (2014) - [j28]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: 627-644 (2014) - [i1]Jerome Bonelle, Alexandre Ern:
Analysis of Compatible Discrete Operator Schemes for the Stokes Equations on Polyhedral Meshes. CoRR abs/1401.7842 (2014) - 2013
- [j27]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): 773-793 (2013) - [j26]Alexandre Ern, Jean-Luc Guermond:
Weighting the Edge Stabilization. SIAM J. Numer. Anal. 51(3): 1655-1677 (2013) - [j25]Alexandre Ern, Martin Vohralík
:
Adaptive Inexact Newton Methods with A Posteriori Stopping Criteria for Nonlinear Diffusion PDEs. SIAM J. Sci. Comput. 35(4) (2013) - 2012
- [j24]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) - 2011
- [j23]David Doyen, Alexandre Ern:
Analysis of the Modified Mass Method for the Dynamic Signorini Problem with Coulomb Friction. SIAM J. Numer. Anal. 49(5): 2039-2056 (2011) - [j22]David Doyen, Alexandre Ern, Serge Piperno
:
Time-Integration Schemes for the Finite Element Dynamic Signorini Problem. SIAM J. Sci. Comput. 33(1): 223-249 (2011) - 2010
- [j21]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): 114-130 (2010) - [j20]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): 491-506 (2010) - [j19]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): 6485-6511 (2010) - [j18]Simona Perotto, Alexandre Ern, Alessandro Veneziani:
Hierarchical Local Model Reduction for Elliptic Problems: A Domain Decomposition Approach. Multiscale Model. Simul. 8(4): 1102-1127 (2010) - [j17]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): 1303-1330 (2010) - [j16]Alexandre Ern, Martin Vohralík
:
A Posteriori Error Estimation Based on Potential and Flux Reconstruction for the Heat Equation. SIAM J. Numer. Anal. 48(1): 198-223 (2010) - [j15]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): 2019-2042 (2010)
2000 – 2009
- 2009
- [j14]Boujemâa Achchab, Mohamed El Fatini
, Alexandre Ern, Ali Souissi:
A posteriori error estimates for subgrid viscosity stabilized approximations of convection-diffusion equations. Appl. Math. Lett. 22(9): 1418-1424 (2009) - [j13]Anne Bourlioux, Alexandre Ern, Pascal Turbis:
A Posteriori Error Estimation for Subgrid Flamelet Models. Multiscale Model. Simul. 8(2): 481-497 (2009) - 2008
- [j12]Alexandre Ern, Jean-Luc Guermond:
Discontinuous Galerkin Methods for Friedrichs' Systems. Part III. Multifield Theories with Partial Coercivity. SIAM J. Numer. Anal. 46(2): 776-804 (2008) - [j11]Daniele A. Di Pietro
, Alexandre Ern, Jean-Luc Guermond:
Discontinuous Galerkin Methods for Anisotropic Semidefinite Diffusion with Advection. SIAM J. Numer. Anal. 46(2): 805-831 (2008) - 2007
- [j10]Erik Burman
, Alexandre Ern:
Continuous interior penalty hp-finite element methods for advection and advection-diffusion equations. Math. Comput. 76(259): 1119-1140 (2007) - 2006
- [j9]Alexandre Ern, Jean-Luc Guermond:
Discontinuous Galerkin Methods for Friedrichs' Systems. I. General theory. SIAM J. Numer. Anal. 44(2): 753-778 (2006) - [j8]Alexandre Ern, Jean-Luc Guermond:
Discontinuous Galerkin Methods for Friedrichs' Systems. Part II. Second-order Elliptic PDEs. SIAM J. Numer. Anal. 44(6): 2363-2388 (2006) - 2005
- [j7]Alexandre Ern, Jennifer Proft:
A posteriori discontinuous Galerkin error estimates for transient convection-diffusion equations. Appl. Math. Lett. 18(7): 833-841 (2005) - [j6]Jean-Pierre Croisille, Alexandre Ern, Tony Lelièvre, Jennifer Proft:
Analysis and simulation of a coupled hyperbolic/parabolic model problem. J. Num. Math. 13(2): 81-103 (2005) - [j5]Erik Burman
, Alexandre Ern:
Stabilized Galerkin approximation of convection-diffusion-reaction equations: discrete maximum principle and convergence. Math. Comput. 74(252): 1637-1652 (2005) - 2003
- [j4]Malte Braack, Alexandre Ern:
A Posteriori Control of Modeling Errors and Discretization Errors. Multiscale Model. Simul. 1(2): 221-238 (2003)
1990 – 1999
- 1997
- [j3]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): 225-236 (1997) - 1996
- [p1]Craig C. Douglas, Alexandre Ern, Mitchell D. Smooke:
Numerical Simulation of Laminar Diffusion Flames. Applications on Advanced Architecture Computers 1996: 243-254 - 1995
- [j2]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): 167-186 (1995) - 1994
- [j1]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): 681-703 (1994)
Coauthor Index
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