Alexandre Ern
		CERMICS , ENPC (Ecole des Ponts) 6 et 8, av. Blaise Pascal 77455 Marne la Vallée cedex 2, France and SERENA Project-Team, INRIA Paris, France e-mail: alexandre.ern(AT)enpc.fr tél: 33 - 1 64 15 35 70 fax: 33 - 1 64 15 35 86

Current position

• Researcher at CERMICS since 1995, Senior Researcher since 2011
• Joint Senior Researcher at INRIA in the SERENA team (since 2016)
• Professor at Ecole des Ponts (since 1997), Associate Professor at Ecole Polytechnique (2010-22)
• Head of Master (M2) Program on Applied Mathematics at Ecole des Ponts (since 2015)
• Co-Editor in Chief
  • IMA Journal of Numerical Analysis (IMAJNA) (since 2024, Associate Editor since 2016)
• Associate Editor
  • SIAM Journal on Scientific Computing (SISC) (since 2011)
  • ESAIM Mathematical Modelling and Numerical Analysis (M2AN) (since 2013)
  • Computational Methods in Applied Mathematics (CMAM, De Gruyter) (since 2016)
  • Journal of Scientific Computing (JOMP, Springer) (since 2020)

Research interests

• Numerical methods (finite elements, dG, structure-preserving discretizations), a posteriori error estimates
• Fluid and solid mechanics, environmental flows (hydrology, porous media)
• List of publications (with preprint or pdf available mostly from 2009, else simply send me an email)
• Some recent talks
  • Penn State online seminar 2020, Polynomial liftings in H¹ and H(div) [pdf]
  • ICOSAHOM Vienna 2021, Hybrid high-order methods for the wave equation [pdf]
  • One-World Numerical Analysis Seminar, April 2022, Hybrid high-order methods for the biharmonic problem [pdf]
  • WIAS workshop, July 2022, A new perspective on time-stepping methods: Beyond strong stability [pdf]
  • ECCOMAS-MFET, August 2023, Hybrid high-order methods for the wave equation [pdf]
  • Numerical methods for evolutionary PDEs, September 2023, Invariant-domain-preserving Runge-Kutta methods [pdf]
  • European Finite Element Fair, June 2024, Third-order A-stable alternating implicit Runge-Kutta schemes [pdf]
  • Von Mises Lecture, July 2024, On the discontinuous Galerkin approximation to Maxwell's equations [pdf]
  • Forth Workshop on Evolution Equations, September 2025, Convergence of ERK-dG approximations of the first-order form of Maxwell's equations with low regularity [pdf]
  • Mittag-Leffler Institut, September 2025, Unfitted HHO methods [pdf]

Finite element trilogy

• Volume I: Approximation and Interpolation (TAM vol. 72) [Springer link] [hal]
• Volume II: Galerkin Approximation, Elliptic and Mixed PDEs (TAM vol. 73) [Springer link] [hal]
• Volume III: First-Order and Time-Dependent PDEs (TAM vol. 74) [Springer link] [hal]
• ... and there is a Volume IV with the Solution to all the exercises [hal]

Other books

• M. Cicuttin, AE, N. Pignet, Hybrid high-order methods. A primer with application to solid mechanics, SpingerBriefs in Mathematics, 2021 [Springer link] [hal] [arXiv]
• D. A. Di Pietro and AE, Mathematical Aspects of Discontinuous Galerkin Methods, vol. 69 SMAI Mathématiques et Applications, Springer, 2012 [Springer link]
• AE and J.-L. Guermond, Theory and Practice of Finite Elements, vol. 159 of Applied Mathematical Series, Springer, New York, 2004 [Springer link]
• AE, Aide-mémoire des éléments finis, Dunod/L'Usine Nouvelle, 2005 [ISBN 2-100-07303-6, 360 p.]
• AE and J.-L. Guermond, Eléments finis: théorie, applications, mise en oeuvre, vol. 36 SMAI Mathématiques et Applications, Springer, Heidelberg, 2002 [ISBN 3-540-42615-9, ix+430 p.]
• AE and V. Giovangigli, Multicomponent Transport Algorithms, vol. m24 of Lecture Notes in Physics, New Series Monographs, Springer-Verlag, Heidelberg, 1994 [ISBN 3-540-58309-2, xiv+427 p.] [Download] [Erratum]

Current post-docs and PhD students

• Rekha Khot (01/2024-12/2025) postdoc on HHO methods for wave propagation and BEM coupling
  PhD students (start date, advisor(s), funding)
• Romain Mottier (11/2021-, A. Ern, CEA/DAM) Unfitted HDG/HHO methods for geophysical wave propagation
• Zuodong Wang (10/2022-, Z. Dong and A. Ern, INRIA) Finite element methods for hyperbolic and degenerate parabolic problems
• Abbas Kabalan (11/2022-, V. Ehrlacher and A. Ern, Safran) Model order reduction for nonparametrized geometrical variability

Industrial partners

• CEA, EDF (current)
• ANDRA, BRGM, EADS, IFPEN (past)

Past post-docs and PhD students

• Omar Durán (11/2019-12/2020)
• Kenan Kergrene (12/2018-08/2020, with M. Vohralik)
• Guillaume Delay (09/2018-08/2019)
• Mohammad Zakerzadeh (10/2017-07/2019, with M. Vohralik)
• Théophile Chaumont (02/2018-09/2018)
• Matteo Cicuttin (02/2016-04/2018)
• Thomas Boiveau (05/2016-09/2017)
• Iain Smears (09/2015-09/2017, with M. Vohralik) [Starting Research Position, INRIA Paris]
• Pablo Tassi (05/2007-10/2009)
• Daniele Di Pietro (02/2006 - 04/2007)
• Karim Djadel (03/2005 - 08/2006)
• Héloise Beaugendre (10/2003 - 12/2004)
• Jennifer Proft (10/2002 - 09/2003)

[their future is academia (9), industry (4)]

• Morgane Steins (05/12/2023, A. Ern and O. Jamond, CEA/DES) An explicit hybrid high-order method for structural dynamics
• Stefano Piccardo (04/12/2023, A. Ern, A. Huerta and M. Giacomini, ENPC and UPC) Simulation of two-fluid immiscible Stokes flows using hybrid nonconforming methods and geometrically unfitted meshes [thesis]
• Idrissa Niakh (14/12/2022, A. Ern and V. Ehrlacher, EDF) Model reduction for variational inequalities in computational mechanics [thesis]
• Riccardo Milani (16/12/2020, A. Ern, EDF) Compatible Discrete Operator schemes for the unsteady incompressible Navier-Stokes equations [thesis]
• Ani Miraci (14/12/2020, M. Vohralik and A. Ern (co-dir), ERC Gatipor) A-posteriori-steered and adaptive p-robust multigrid solvers
• Frédéric Marazzato (29/05/2020, A. Ern and K. Sab (co-dir), CEA) Discrete element and time-integration methods for elasto-plasticity and dynamic cracking [thesis]
• Nicolas Pignet (22/10/2019, A. Ern, EDF) Hybrid High-Order methods for nonlinear solid mechanics [thesis] [Paul Caseau prize 2020] [nominee of AMIES 2020 prize]
• Patrik Daniel (22/03/2019, M. Vohralik and A. Ern (co-dir), ERC Gatipor) Éléments finis hp-adaptatifs avec contraction d'erreur garantie et solveurs multi-niveaux inexacts
• Amina Benaceur (21/12/2018, A. Ern and V. Ehrlacher, EDF) Model reduction for nonlinear heat transfer and mechanics [thesis]
• Karol Cascavita (18/12/2018, X. Chateau (co-dir) and A. Ern, Labex MMCD) Hybrid discretization methods for Signorini contact and Bingham flow problems [thesis]
• Rita Riedlbeck (11/2017, D. Di Pietro and A. Ern (co-dir), EDF) Adaptive algorithms for poromechanics and poroplasticity
• Yannick Masson (06/2017, A. Ern and O. Baverel (co-dir), Labex MMCD) Tchebyshev nets and application to Grid Shells
• Pierre Cantin (11/2016, A. Ern, EDF) Approximation of scalar and vector transport problems on polyhedral meshes
• Jérôme Bonelle (11/2014, A. Ern, EDF) Compatible discrete operator schemes on polyhedral meshes for elliptic and Stokes equations [ENPC best PhD award]
• Maria Adela Puscas (10/2014, A. Ern and C. Tenaud (co-dir), CEA/DAM) Conservative coupling method between an inviscid compressible fluid and a 3D fragmentable structure
• Christelle Lusso (12/2013, A. Ern and F. Bouchut (co-dir), ENPC) Numerical modelling of gravitational viscoplastic flows with fluid/solid transition
• Fabien Casenave (12/2013, A. Ern and T. Lelièvre (co-dir), French Ministry (MEDDE) and EADS IW) Model reduction methods applied to aeroacoustic problems solved by integral equations
• Nancy Chalhoub (12/2012, A. Ern and M. Vohralik (co-dir), ENPC and CNRS Lebanon) A posteriori error estimates for finite volume approximations of the time-dependent convection-diffusion-reaction equation
• Marie Rousseau (12/2012, A. Ern and O. Le Maitre (co-dir), ENPC and BRGM) Uncertainty propagation and sensitivity analysis for infiltration and erosion modeling
• Rémi Joubaud (11/2012, A. Ern and T. Lelièvre (co-dir), ANDRA) Mathematical and numerical modeling of fluids at nanometric scale [UPE best PhD award]
• Julie Tryoen (11/2011, A. Ern and O. Le Maitre (co-dir), ENPC) Adaptive stochastic Galerkin methods for uncertainty propagation in hyperbolic systems
• David Doyen (12/2010, A. Ern and S. Piperno (co-dir), EDF) Dynamic crack propagation with cohesive forces
• Pierre Sochala (12/2008, A. Ern and S. Piperno (co-dir), ENPC) Discontinuous Galerkin methods for Richards's equation and its coupling to kinematic wave equations
• Annette Stephansen (12/2007, A. Ern, ANDRA) A posteriori error estimates and Discontinuous Galerkin methods
• Sébastien Meunier (11/2007, A. Ern, EDF) Time-space a posteriori error estimates for poroelasticity
• Pierre Tardif d'Hamonville (12/2006, A. Ern and L. Dormieux (co-dir), ENPC) Diffusion and dispersion in 3D sphere networks
• Linda El Alaoui (01/2005, A. Ern, ENPC) A posteriori error estimates for mixed and nonconforming finite element methods
• Emmanuel Bongiovanni (12/2002, A. Ern and N. Glinsky, ENPC) Relaxation methods for Navier-Stokes equations

[their future is academia (8), industry (20)]