List of Publications

Alexandre Ern

• Recent preprints

  • F. Bouchut, C. Carstensen and AE, H¹ regularity of the inviscid total variation and Bingham minimisers for H¹ data [hal]

  • T. Chaumont-Frelet and AE, Asymptotic optimality of the edge finite element approximation of the time-harmonic Maxwell's equations [hal]

  • T. Chaumont-Frelet and AE, Damped energy-norm a posteriori error estimates for fully discrete approximations of the wave equation using C²-reconstructions [hal] [arXiv]

  • AE and J.-L. Guermond, Spectral correctness of the discontinuous Galerkin approximation of the first-order form of Maxwell's equations with discontinuous coefficients [hal]

  • AE and J.-L. Guermond, Spectral correctness of the continuous finite element stabilized approximation of the first-order form of Maxwell's equations [hal]

  • AE and J.-L. Guermond, Third-order A-stable alternating implicit Runge-Kutta schemes [hal]

  • AE, J.-L. Guermond and Z. Wang, Asymptotic and invariant-domain preserving schemes for scalar conservation equations with stiff source terms and multiple equilibrium points [hal]

  • AE and M. Steins, Convergence analysis for the wave equation discretized with hybrid methods in space (HHO, HDG and WG) and the leapfrog scheme in time [hal]

• 2024

  • Z. Dong and AE, C⁰-hybrid high-order methods for biharmonic problems, IMA J. Numer. Anal., 44(1), 24-57 (2024) [hal] [arXiv]

  • I. Niakh, G. Drouet, V. Ehrlacher, and AE, A reduced basis method for frictional contact problems formulated with Nitsche's method, to appear in SMAI J. Comput. Math. [hal]

• 2023

  • E. Burman, G. Delay and AE, 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) [hal] [pdf, copyright SIAM]

  • E. Burman, G. Delay, AE and L. Oksanen, A stability estimate for data assimilation subject to the heat equation with initial datum, Comptes Rendus Math. (CRAS), 361, 1521-1530 (2023) [hal]

  • Z. Dong, AE and J.-L. Guermond, Local decay rates of best-approximation errors using vector-valued finite elements for fields with low regularity and integrable curl or divergence, Comptes Rendus Math. (CRAS), 361, 723-736 (2023) [hal] [arXiv] [doi]

  • AE and J.-L. Guermond, Invariant-domain-preserving high-order time stepping: II. IMEX schemes, SIAM J. Sci. Comput., 45(5), A2511-A2538 (2023) [hal] [pdf, copyright SIAM]

  • AE and J.-L. 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) [hal]

  • I. Niakh, G. Drouet, V. Ehrlacher, and AE, Stable model reduction for linear variational inequalities with parameter-dependent constraints, ESAIM Math. Mod. Numer. Anal., 57(1), 167-189 (2023) [hal]

  • S. Piccardo and AE, Surface tension effects between two immiscible Stokes fluids: a computational study using unfitted hybrid high-order methods and a level-set scheme, SMAI J. Comput. Math., 9, 257-283 (2023) [hal]

  • M. Steins, AE, O. Jamond and F. Drui, Time-explicit Hybrid High-Order method for the nonlinear acoustic wave equation, ESAIM Math. Mod. Numer. Anal., 57(5), 2977-3006 (2023) [pdf, copyright EDP Sciences and SMAI] [hal]

• 2022

  • E. Burman, O. Duran, AE, Hybrid high-order methods for the acoustic wave equation in the time domain, Commun. Appl. Math. Comput. (CAMC), 4(2), 597-633 (2022) [hal]

  • E. Burman, O. Duran, AE, Unfitted hybrid high-order methods for the wave equation, Comp. Meth. Appl. Mech. Eng., 389, 114366 (2022) [hal]

  • T. Chaumont-Frelet, AE, S. Lemaire and F. Valentin, Bridging the Multiscale Hybrid-Mixed and Multiscale Hybrid High-Order methods, ESAIM Math. Mod. Numer. Anal., 56, 261-285 (2022) [hal] [pdf, copyright EDP Sciences and SMAI]

  • T. Chaumont-Frelet, AE and M. Vohralík, Stable broken H(curl) polynomial extensions and p-robust a posteriori error estimates by broken patchwise equilibration for the curl-curl problem, Math. Comp., 91(333), 37-74 (2022) [hal] [pdf, copyright AMS]

  • Z. Dong and AE, Hybrid high-order and weak Galerkin methods for the biharmonic problem, SIAM J. Numer. Anal., 60(5), 2626-2656 (2022) [pdf, copyright SIAM] [hal] [arXiv]

  • AE, T. Gudi, I. Smears and M. Vohralík, Equivalence of local-and global-best approximations, a simple stable local commuting projector, and optimal hp approximation estimates in H(div), IMA J. Numer. Anal., 42(2), 1023-1049 (2022) [hal] [arXiv]

  • AE and J.-L. Guermond, Invariant-domain-preserving high-order time stepping: I. Explicit Runge-Kutta schemes, SIAM J. Sci. Comput., 44(5), A3366-A3392 (2022) [hal] [pdf, copyright SIAM]

  • AE and J.-L. 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) [hal] [Springer link] [pdf]

  • AE, F. Hédin, G. Pichot and N. Pignet, Hybrid high-order methods for flow simulations in extremely large discrete fracture networks, SMAI J. Comp. Math., 8, 375-398 (2022) [hal] [pdf]

  • F. Marazzato, AE and L. Monasse, Quasi-static crack propagation with a Griffith criterion using a variational discrete element method, Comput. Mech., 69(2), 527-539 (2022) [hal] [arXiv]

  • R. Milani, J. Bonelle and AE, 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) [hal]

• 2021

  • E. Burman, M. Cicuttin, G. Delay and AE, An unfitted hybrid high-order method with cell agglomeration for elliptic interface problems, SIAM J. Sci. Comput., 43(2), A859-A882 (2021) [pdf, copyright SIAM] [hal]

  • E. Burman, G. Delay and AE, An unfitted hybrid high-order method for the Stokes interface problem, IMA J. Numer. Anal., 41(4), 2362-2387 (2021) [hal]

  • E. Burman, G. Delay and AE, A hybridized high-order method for unique continuation subject to the Helmholtz equation, SIAM J. Numer. anal., 59(5), 2368-2392 (2021) [pdf, copyright SIAM] [hal]

  • E. Burman, O. Duran, AE and M. Steins, Convergence analysis of hybrid high-order methods for the wave equation, J. Sci. Comput., 87(3), 91 (2021) [hal] [journal link]

  • C. Carstensen, AE and S. Puttkammer, Guaranteed lower bounds on eigenvalues of elliptic operators with a hybrid high-order method, Numer. Math., 149(2) 273-304 (2021) [hal] [Springer link]

  • T. Chaumont-Frelet, AE and M. Vohralík, On the derivation of guaranteed and p-robust a posteriori error estimates for the Helmholtz equation, Numer. Math., 148(3), 525-573 (2021) [hal] [Springer link]

  • Q. Deng and AE, SoftFEM: revisiting the spectral finite element approximation of elliptic operators, Comput. Math. Appl., 101, 119-133 (2021) [arXiv] [hal]

  • Z. Dong and AE, Hybrid high-order method for singularly perturbed fourth-order problems on curved domains, ESAIM Math. Mod. Numer. Anal., 55, 3091-3114 (2021) [doi]

  • AE, M. Vohralík and M. Zakerzadeh, Guaranteed and robust L²-norm a posteriori error estimates for 1D linear advection problems, ESAIM Math. Mod. Numer. Anal., 55, S447-S474 (2021) [hal]

  • C. Lusso, F. Bouchut, AE, and A. Mangeney, Explicit solutions to a free boundary model for the static/flowing transition in thin granular flows, ESAIM Math. Mod. Numer. Anal., 55, S369-S395 (2021) [hal]

• 2020

  • A. Benaceur, V. Ehrlacher and AE, A reduced basis method for parametrized variational inequalities applied to contact mechanics, Int. J. Numer. Methods Eng., 121(6), 1170-1197 (2020) [hal] [doi]

  • V. Calo, AE, I. Muga and S. Rojas, An adaptive stabilized conforming finite element method via residual minimization on dual discontinuous Galerkin norms, Comp. Meth. Appl. Mech. Eng., 363, 112891 (2020) [hal] [arXiv] [doi]

  • K. Cascavita, F. Chouly and AE, Hybrid high-order discretizations combined with Nitsche's method for Dirichlet and Signorini boundary conditions, IMA J. Numer. Anal., 40, 2189-2226 (2020) [hal]

  • T. Chaumont-Frelet, AE and M. Vohralík, Polynomial-degree-robust H(curl)-stability of discrete minimization in a tetrahedron Comptes Rendus Math. (CRAS), 358(9-10), 1101-1110 (2020) [hal]

  • F. Chouly, AE and M. 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) [hal] [pdf, copyright SIAM]

  • M. Cicuttin, AE and T. Gudi, Hybrid high-order methods for the elliptic obstacle problem, J. Sci. Comput., 83, Paper 8, 18 pp. (2020) [hal] [doi]

  • P. Daniel, AE, and M. Vohralík, An adaptive hp-refinement strategy with inexact solvers and computable guaranteed bound on the error reduction factor, Comp. Meth. Appl. Mech. Eng., 359, 112607 (2020) [hal]

  • AE and M. Vohralík, Stable broken H¹ and H(div) polynomial extensions for polynomial-degree-robust potential and flux reconstruction in three space dimensions, Math. Comp., 89(332), 551-594 (2020) [pdf, copyright AMS] [arXiv] [hal]

  • AE and P. Zanotti, A quasi-optimal variant of the hybrid high-order method for elliptic partial differential equations with H^-1 loads, IMA J. Numer. Anal., 40, 2163-2188 (2020) [hal] [arXiv]

  • F. Marazzato, AE and L. Monasse, A variational discrete element method for quasistatic and dynamic elastoplasticity, Int. J. Numer. Methods Eng., 121, 5295-5319 (2020) [hal] [arXiv]

• 2019

  • M. Abbas, AE and N. Pignet, A hybrid high-order method for incremental associate plasticity with small deformations, Comp. Meth. Appl. Mech. Eng., 346, 891-912 (2019) [hal] [arXiv] [doi]

  • M. Abbas, AE and N. Pignet, A hybrid high-order method for finite elastoplastic deformations within a logarithmic strain framework, Int. J. Numer. Methods Eng., 120, 303-327 (2019) [hal] [doi]

  • T. Boiveau, V. Ehrlacher, AE and A. Nouy, Low-rank approximation of linear parabolic equations by space-time tensor Galerkin methods, ESAIM Math. Mod. Numer. Anal., 53, 635-658 (2019) [pdf, copyright EDP Sciences and SMAI] [hal] [arXiv]

  • V. Calo, M. Cicuttin, Q. Deng and AE, Spectral approximation of elliptic operators by the hybrid high-order method, Math. Comp., 88(318), 1559-1586 (2019) [pdf, copyright AMS] [hal] [arXiv]

  • M. Cicuttin, AE and S. Lemaire, A hybrid high-order method for highly oscillatory elliptic problems, Comput. Methods Appl. Math., 19(4), 723-748 (2019) [hal] [arXiv]

  • AE, I. Smears, and M. Vohralík, Equilibrated flux a posteriori error estimates in L²(H¹)-norms for high-order discretizations of parabolic problems, IMA J. Numer. Anal., 39(3), 1158-1179 (2019) [arXiv] [hal]

  • F. Marazzato, AE, C. Mariotti and L. Monasse, An explicit pseudo-energy conserving time-integration scheme for Hamiltonian dynamics, Comp. Meth. Appl. Mech. Eng., 347, 906-927 (2019) [hal] [doi]

• 2018

  • M. Abbas, AE and N. Pignet, Hybrid high-order methods for finite deformations of hyperelastic materials, Comput. Mech., 62(4), 909-938 (2018) [hal] [arXiv]

  • A. Benaceur, V. Ehrlacher, AE and S. Meunier, A progressive reduced basis/empirical interpolation method for nonlinear parabolic problems, SIAM J. Sci. Comput., 40(5), A2930-A2955 (2018) [pdf, copyright SIAM] [hal] [arXiv]

  • E. Burman and AE, An unfitted hybrid high-order method for elliptic interface problems, SIAM J. Numer. Anal., 56(3), 1525-1546 (2018) [pdf, copyright SIAM] [hal]

  • K. Cascavita, J. Bleyer, X. Chateau and AE, Hybrid discretization methods with adaptive yield surface detection for Bingham pipe flows, J. Sci. Comput., 77(3), 1424-1443 (2018) [hal]

  • M. Cicuttin, D. A. Di Pietro and AE, Implementation of Discontinuous Skeletal methods on arbitrary-dimensional, polytopal meshes using generic programming, J. Comput. Appl. Math., 344, 852-874 (2018) [hal] [doi]

  • P. Daniel, AE, I. Smears, and M. Vohralík, An adaptive hp-refinement strategy with computable guaranteed bound on the error reduction factor, Comput. Math. Appl., 76(5), 967-983 (2018) [hal] [arXiv] [doi]

  • AE and J.-L. Guermond, Analysis of the edge finite element approximation of the Maxwell equations with low regularity solutions, Comput. Math. Appl., 75(3), 918-932 (2018) [arXiv] [hal]

  • AE and J.-L. 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) [hal]

• 2017

  • E. Burman and AE, A nonlinear consistent penalty method for positivity preservation in the finite element approximation of the transport equation, Comp. Meth. Appl. Mech. Eng., 320, 122-132 (2017) [hal]

  • E. Burman, AE and M. Fernández, Fractional-step methods and finite elements with symmetric stabilization for the transient Oseen problem, ESAIM Math. Mod. Numer. Anal., 51(2), 487-507 (2017) [pdf, copyright EDP Sciences and SMAI]

  • P. Cantin and AE, An edge-based scheme on polyhedral meshes for vector advection-reaction equations, ESAIM Math. Mod. Numer. Anal., 51(5), 1561-1581 (2017) [pdf, copyright EDP Sciences and SMAI] [doi] [hal]

  • D. Di Pietro and AE, Arbitrary-order mixed methods for heterogeneous anisotropic diffusion on general meshes, IMA J. Numer. Anal., 37(1), 40-63 (2017) [hal]

  • AE and J.-L. Guermond, Finite element quasi-interpolation and best approximation, ESAIM Math. Mod. Numer. Anal., 51(4), 1367-1385 (2017) [pdf, copyright EDP Sciences and SMAI] [doi]

  • AE, I. Smears, and M. Vohralík, Discrete p-robust H(div)-liftings and a posteriori estimates for H^-1 source terms, Calcolo, 54(3), 1009-1025 (2017) [arXiv] [hal] [journal link]

  • AE, I. Smears, and M. 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) [pdf, copyright SIAM] [doi] [arXiv] [hal]

  • C. Lusso, F. Bouchut, AE and A. Mangeney, A free interface model for static/flowing dynamics in thin-layer flows of granular materials with yield: simple shear simulations and comparison with experiments Appl. Sci., 7, 386-412 (2017) [hal] [pdf]

  • C. Lusso, AE, F. Bouchut, A. Mangeney, M. Farin and O. 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) [hal]

  • R. Riedlbeck, D. Di Pietro, AE, S. Granet, K. 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) [hal]

• 2016

  • L. Beirão da Veiga and AE, Preface to the Special Issue on Polyhedral discretization for PDEs, ESAIM Math. Mod. Numer. Anal., 50(3), 633-634 (2016) [pdf, copyright EDP Sciences and SMAI]

  • P. Cantin, J. Bonelle, E. Burman and AE, A vertex-based scheme on polyhedral meshes for advection-reaction equations with sub-mesh stabilization, Comput. Math. Appl., 72(9), 2057-2071 (2016) [hal]

  • P. Cantin and AE, Vertex-based Compatible Discrete Operator Schemes on polyhedral meshes for advection-diffusion equations, Comput. Methods Appl. Math., 16(2), 187-212 (2016) [hal]

  • F. Casenave, AE and T. Lelièvre, Variants of the Empirical Interpolation Method: Symmetric formulation, choice of norms and rectangular extension Appl. Math. Letters, 56, 23-28 (2016) [arXiv] [doi]

  • B. Cockburn, D. Di Pietro and AE, Bridging the hybrid high-order and hybridizable discontinuous Galerkin methods, ESAIM Math. Mod. Numer. Anal., 50(3), 635-650 (2016) [pdf, copyright EDP Sciences and SMAI] [hal]

  • D. Di Pietro, AE and S. Lemaire, A review of hybrid high-order methods: formulations, computational aspects, comparison with other methods, In Building Bridges: Connections and Challenges in Modern Approaches to Numerical Partial Differential Equations, G. R. Barrenechea, F. Brezzi, A. Cangiani, E. H. Georgoulis Eds., Lec. Notes Comput. Sci. Engrg., 114, pp. 205-236, Springer, (2016) [hal]

  • D. Di Pietro, AE, A. Linke and F. Schieweck, A discontinuous skeletal method for the viscosity-dependent Stokes problem, Comp. Meth. Appl. Mech. Eng. 306, 175-195 (2016) [hal]

  • V. Dolejší, AE and M. Vohralík, hp-adaptation driven by polynomial-degree-robust a posteriori error estimates for elliptic problems, SIAM J. Sci. Comput. 38(5), A3220-A3246 (2016) [pdf, copyright SIAM]

  • AE and J.-L. Guermond, Mollification in strongly Lipschitz domains with application to continuous and discrete De Rham complexes, Comput. Methods Appl. Math., 16(1), 51-75 (2016) [hal] [arXiv]

  • AE and J.-L. Guermond, A converse to Fortin's lemma in Banach spaces, C. R. Math. Acad. Sci. Paris, 354, 1092-1095 (2016) [pdf, doi 10.1016/j.crma.2016.09.013] [hal]

  • AE and J.-L. Guermond, Linear stabilization for first-order PDEs, in Handbook of Numerical Methods for Hyperbolic Problems. Basic and Fundamental Issues, R. Abgrall and C.-W. Shu, Eds., Handbook of Numerical Analysis, 17, pp. 265-288, North-Holland, Amsterdam (2016) [preprint]

  • AE and F. Schieweck, Discontinuous Galerkin method in time combined with a stabilized finite element method in space for linear first-order PDEs, Math. Comp., 85(301), 2099-2129 (2016) [pdf, copyright AMS]

• 2015

  • J. Bonelle, D. Di Pietro and AE, Low-order reconstruction operators on polyhedral meshes: Application to Compatible Discrete Operator schemes, Comput. Aided Geom. D., 35/36, 27-41 (2015) [hal]

  • J. Bonelle and AE, Analysis of compatible discrete operator schemes for the Stokes equations on polyhedral meshes, IMA J. Numer. Anal. 35, 1672-1697 (2015) [hal] [journal link]

  • F. Casenave, AE, and T. Lelièvre, A nonintrusive Reduced Basis Method applied to aeroacoustic simulations, Advances Comput. Math. 41, 961-986 (2015) [arXiv] [doi 10.1007/s10444-014-9365-0]

  • L. Contento, AE and R. Vermiglio, A linear-time approximate convex envelope algorithm using the double Legendre-Fenchel transform with application to phase separation, Comput. Optim. Appl., 60, 231-261 (2015) [hal] [journal link]

  • D. Di Pietro, J. Droniou and AE, A discontinuous-skeletal method for advection-diffusion-reaction on general meshes, SIAM J. Numer. Anal., 53(5), 2135-2157 (2015) [pdf, copyright SIAM]

  • D. Di Pietro and AE, A hybrid high-order locking-free method for linear elasticity on general meshes, Comp. Meth. Appl. Mech. Eng., 283, 1-21 (2015) [hal]

  • D. Di Pietro and AE, Hybrid high-order methods for variable-diffusion problems on general meshes, C. R. Math. Acad. Sci. Paris, 353, 31-34 (2015) [hal]

  • D. Di Pietro and AE, Equilibrated tractions for the hybrid high-order method, C. R. Math. Acad. Sci. Paris, 353, 279-282 (2015) [hal]

  • AE and M. 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) [pdf, copyright SIAM]

  • A. Puscas, L. Monasse, AE, C. Tenaud and C. Mariotti, A conservative immersed boundary method for an inviscid compressible flow coupled with a fragmenting structure, Int. J. Numer. Methods Engrg., 103(13), 970-995 (2015) [hal]

  • A. Puscas, L. Monasse, AE, C. Tenaud, C. Mariotti and V. Daru, A time semi-implicit scheme for the energy-balanced coupling of a shocked fluid flow with a deformable structure , J. Comput. Phys., 296(1), 241-262 (2015) [hal]

• 2014

  • J. Bonelle and AE, Analysis of compatible discrete operator schemes for elliptic problems on polyhedral meshes, ESAIM Math. Mod. Numer. Anal., 48, 553-581 (2014) [pdf, copyright EDP Sciences and SMAI]

  • F. Casenave, AE, and T. Lelièvre, Accurate and online-efficient evaluation of the a posteriori error bound in the reduced basis method, ESAIM Math. Mod. Numer. Anal., 48, 207-229 (2014) [pdf, copyright EDP Sciences and SMAI]

  • F. Casenave, AE and G. Sylvand, Coupled BEM/FEM for the convected Helmholtz equation with non-uniform flow in a bounded domain, J. Comput. Phys., 257(Part A), 627-644 (2014) [arXiv]

  • D. Di Pietro, AE and S. 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) [doi]

  • R. Joubaud, O. Bernard, A. Delville, AE, B. Rotenberg, and P. Turq, Numerical study of density functional theory with mean spherical approximation for ionic condensation in highly charged confined electrolytes, Phys. Rev. E, 89, 062302 (2014) [pdf, copyright APS]

• 2013

  • V. Dolejší, AE, and M. Vohralík, A framework for robust a posteriori error control in unsteady nonlinear advection-diffusion problems, SIAM J. Numer. Anal., 51(2), 773-793 (2013) [pdf, copyright SIAM]

  • D. Doyen, AE, and S. Piperno, Quasi-explicit time-integration schemes for dynamic fracture with set-valued cohesive zone models, Comput. Mech., 52(2), 401-416 (2013)

  • AE and J.-L. Guermond, Weighting the edge stabilization, SIAM J. Numer. Anal., 51(3), 1655-1677 (2013) [pdf, copyright SIAM]

  • AE and M. Vohralík, Four closely related equilibrated flux reconstructions for nonconforming finite elements, C. R. Math. Acad. Sci. Paris, 351, 77-80 (2013) [hal]

  • AE and M. Vohralík, Adaptive inexact Newton methods with a posteriori stopping criteria for nonlinear diffusion PDEs, SIAM J. Sci. Comput., 35(4), A1761-A1791 (2013) [pdf, copyright SIAM]

  • AE and M. Vohralík, Adaptive inexact Newton methods: a posteriori error control and speed-up of calculations, Siam News, 46, 1, (2013).

• 2012

  • E. Burman and AE, Implicit-Explicit Runge-Kutta schemes and finite elements with symmetric stabilization for advection-diffusion equations, ESAIM Math. Mod. Numer. Anal., 46, 681-707 (2012) [pdf, copyright EDP Sciences and SMAI]

  • D. Di Pietro and AE, Analysis of a discontinuous Galerkin method for heterogeneous diffusion problems with low-regularity solutions, Numer. Methods Partial Differ. Equations, 28, 1161-1171 (2012) [preprint]

  • AE, R. Joubaud, and T. Lelièvre, Mathematical study of non-ideal electrostatic correlations in equilibrium electrolytes, Nonlinearity, 25, 1635-1652 (2012) [pdf, copyright IOP Publishing]

  • AE and I. Mozolevski, Discontinuous Galerkin method for two-component liquid-gas porous media flows, Comput. Geosci., 16, 677-690 (2012) [preprint]

  • M. Rousseau, O. Cerdan, AE, O. Le Maitre and P. Sochala, Study of overland flow with uncertain infiltration using stochastic tools, Adv. Water Res., 38, 1-12 (2012) [preprint]

  • J. Tryoen, O. Le Maitre, and AE, Adaptive anisotropic spectral stochastic methods for uncertain scalar conservation laws, SIAM J. Sci. Comput., 34(5), A2459-A2481 (2012) [pdf, copyright SIAM]

• 2011
  • D. Doyen and AE, Analysis of the modified mass method for the dynamic Signorini problem with Coulomb friction, SIAM J. Numer. Anal., 49(5), 2039-2056 (2011) [pdf, copyright SIAM]

  • D. Doyen, AE and S. Piperno, Time-integration schemes for the finite element dynamic Signorini problem, SIAM J. Sci. Comput., 33(1), 223-249 (2011) [pdf, copyright SIAM]

  • L. El Alaoui, AE and M. Vohralík, Guaranteed and robust a posteriori error estimates and balancing discretization and linearization errors for monotone nonlinear problems, Comp. Meth. Appl. Mech. Eng., 200, 2782-2795 (2011) [preprint]

  • AE, R. Joubaud and T. Lelièvre, Numerical study of a thin liquid film flowing down an inclined wavy plane, Physica D, 240, 1714-1723 (2011) [preprint]

• 2010
  • A. Bourlioux, AE and P. Turbis, A posteriori error estimation for subgrid flamelet models, Multiscale Model. Simul., 8(2), 481-497 (2010).

  • E. Burman, AE and M. A. Fern´ndez, 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) [pdf, copyright SIAM]

  • D. A. Di Pietro and AE, Discrete functional analysis tools for Discontinuous Galerkin methods with application to the incompressible Navier--Stokes equations, Math. Comp., 79(271), 1303-1330 (2010) [preprint]

  • D. Doyen, AE and S. Piperno, A three-field augmented Lagrangian formulation of unilateral contact problems with cohesive forces, ESAIM Math. Mod. Numer. Anal., 44(2), 323-346 (2010) [pdf, copyright EDP Sciences and SMAI]

  • AE, I. Mozolevski and L. Schuh, Discontinuous Galerkin approximation of two-phase flows in heterogeneous porous media with discontinuous capillary pressures, Comp. Meth. Appl. Mech. Eng., 199(23-24), 1491-1501 (2010) [preprint]; Corrigendum ibid., 245-246, 348-349 (2012) [preprint]

  • AE, A. F. Stephansen and M. Vohralík, Guaranteed and robust discontinuous Galerkin a posteriori error estimates for convection-diffusion-reaction problems, J. Comput. Appl. Math., 234, 114-130 (2010) [preprint]

  • AE and M. Vohralík, A posteriori error estimation based on potential and flux reconstruction for the heat equation, SIAM J. Numer. Anal., 48(1), 198-223 (2010) [pdf, copyright SIAM]

  • S. Perotto, AE and A. Veneziani, Hierarchical local model reduction for elliptic problems: A domain decomposition approach, Multiscale Model. Simul., 8(4), 1102-1127 (2010).

  • J. Tryoen, O. Le Maitre, M. Ndjinga and AE, Intrusive projection methods with upwinding for uncertain nonlinear hyperbolic systems, J. Comput. Phys., 229, 6485-6511 (2010) [preprint]

  • J. Tryoen, O. Le Maitre, M. Ndjinga and AE, Roe solver with entropy corrector for uncertain hyperbolic systems, J. Comput. Appl. Math., 235, 491-506 (2010) [preprint]

• 2009
  • B. Achchab, M. El Fatini, AE and A. Souissi, A posteriori error estimates for subgrid viscosity stabilized approximations of convection-diffusion equations, Appl. Math. Letters, 22, 1418-1424 (2009).

  • F. Chazel, M. Benoit, AE and S. Piperno, A double-layer Boussinesq-type model for highly nonlinear and dispersive waves, Proc. R. Soc. A, 465, 2319-2346 (2009).

  • D. Doyen and AE, Convergence of a space semi-discrete modified mass method for the dynamic Signorini problem, Comm. Math. Sciences, 7(4), 1063-1074 (2009) [preprint]

  • AE and S. Meunier, A posteriori error analysis of Euler-Galerkin approximations to coupled elliptic-parabolic problems, ESAIM Math. Mod. Numer. Anal., 43, 353-375 (2009) [pdf, copyright EDP Sciences and SMAI]

  • AE, I. Mozolevski and L. Schuh, Accurate velocity reconstruction for Discontinuous Galerkin approximations of two-phase porous media flows, C. R. Math. Acad. Sci. Paris, 347, 551-554 (2009) [preprint]

  • AE, A. F. Stephansen and P. Zunino, A Discontinuous Galerkin method with weighted averages for advection-diffusion equations with locally small and anisotropic diffusivity, IMA J. Numer. Anal., 29(2), 235-256 (2009) [preprint]

  • AE and M. Vohralík, Flux reconstruction and a posteriori error estimation for discontinuous Galerkin methods on general nonmatching grids, C. R. Math. Acad. Sci. Paris, 347, 441-444 (2009) [preprint]

  • P. Sochala, AE and S. Piperno, Mass conservative BDF-discontinuous Galerkin/explicit finite volume schemes for coupling subsurface and overland flows, Comp. Meth. Appl. Mech. Eng., 198, 2122-2136 (2009) [preprint]

• 2008
  • B. Achchab, M. El Fatini, AE and A. Souissi, Adaptive mesh for algebraic orthogonal subscale stabilization of convective dispersive transport, C. R. Math. Acad. Sci. Paris, 346, 1187-1190 (2008).

  • E. Burman and AE, Discontinuous Galerkin approximation with discrete variational principle for the nonlinear Laplacian, C. R. Math. Acad. Sci. Paris, 346(17/18), 1013-1016 (2008).

  • D. Di Pietro, AE and J.-L. Guermond, Discontinuous Galerkin methods for anisotropic semi-definite diffusion with advection, SIAM J. Numer. Anal., 46(2), 805-831 (2008) [pdf, copyright SIAM]

  • AE and J.-L. Guermond, Discontinuous Galerkin methods for Friedrichs' systems. III. Multi-field theories with partial coercivity, SIAM J. Numer. Anal., 46(2), 776-804 (2008) [pdf, copyright SIAM]

  • A. Ern, S. Piperno and K. Djadel, A well-balanced Runge-Kutta Discontinuous Galerkin method for the Shallow-Water Equations with flooding and drying, Int. J. Numer. Meth. Fluids, 58(1), 1-25 (2008) [preprint]

  • AE and A. F. Stephansen, A posteriori energy-norm error estimates for advection-diffusion equations approximated by weighted interior penalty methods, J. Comp. Math., 26(4), 488-510 (2008) [preprint]

• 2007
  • E. Burman and AE, Continuous interior penalty $hp$-finite element methods for advection and advection-diffusion equations, Math. Comp., 76(259), 1119-1140 (2007).

  • E. Burman and AE, A continuous finite element method with face penalty to approximate Friedrichs' systems, ESAIM Math. Mod. Numer. Anal., 41(1), 55-76 (2007).

  • E. Burman, AE, I. Mozolevski and B. Stamm, The symmetric discontinuous Galerkin method does not need stabilization in 1D for polynomial orders p >= 2, C. R. Math. Acad. Sci. Paris, 345, 599-602 (2007).

  • L. El Alaoui, AE and E. Burman, A priori and a posteriori analysis of nonconforming finite elements with face penalty for advection-diffusion equations, IMA J. Numer. Anal., 27(1), 151-171 (2007).

  • AE, J.-L. Guermond and G. Caplain, An intrinsic criterion for the bijectivity of Hilbert operators related to Friedrichs' systems, Comm. Partial Differ. Equations, 32, 317-341 (2007).

  • AE and T. Lelièvre, Adaptive models for polymeric fluid flow simulation, C. R. Math. Acad. Sci. Paris, 344(7), 473-476 (2007).

  • AE, S. Nicaise and M. Vohralík, An accurate H(div) flux reconstruction for discontinuous Galerkin approximations of elliptic problems, C. R. Math. Acad. Sci. Paris, 345, 709-712 (2007) [preprint]

  • P. Tardif d'Hamonville, AE and L. Dormieux, Finite element evaluation of diffusion and dispersion tensors in periodic porous media with advection, Comput. Geosci., 11, 43-58 (2007).

• 2006
  • H. Beaugendre, AE, Th. Esclaffer, E. Gaume, I. Ginzburg and C. Kao, A seepage face model for the interaction of shallow water tables with ground surface: Application of the obstacle-type method, J. Hydrology, 329(1/2), 258-273 (2006).

  • L. Debiane, B. Ivorra, B. Mohammadi, F. Nicoud, T. Poinsot, AE and H. Pitsch, A low-complexity global optimization algorithm for temperature and pollution control in flames with complex chemistry, Int. J. Comput. Fluid Dynamics, 20(2), 93-98 (2006).

  • L. El Alaoui and AE, Nonconforming finite element methods with subgrid viscosity applied to advection-diffusion-reaction equations, Num. Methods Partial Differential Equations, 22(5), 1106-1126 (2006).

  • AE and J.-L. Guermond, Discontinuous Galerkin methods for Friedrichs' systems. I. General theory, SIAM J. Numer. Anal., 44(2), 753-778 (2006) [pdf, copyright SIAM]

  • AE and J.-L. Guermond, Discontinuous Galerkin methods for Friedrichs' systems. II. Second-order elliptic PDE's, SIAM J. Numer. Anal., 44(6), 2363-2388 (2006) [pdf, copyright SIAM]

  • AE and J.-L. Guermond, Evaluation of the condition number in linear systems arising in finite element approximations, ESAIM Math. Mod. Numer. Anal., 40(1), 29-48 (2006).

  • AE and J. Proft, Multi-algorithmic methods for coupled hyperbolic-parabolic problems, Int. J. Numer. Anal. Model., 3(1), 94-114 (2006).

• 2000-2005
  • E. Burman and AE, Stabilized Galerkin approximation of convection-diffusion-reaction equations: discrete maximum principle and convergence, Math. Comp., 74(252), 1637-1652 (2005).
  • J.-P. Croisille, AE, T. Lelièvre and J. Proft, Analysis and simulation of a coupled hyperbolic/parabolic model problem, J. Numer. Math., 13(2), 81-103 (2005).
  • A.S. Dickinson, AE and V. Vesovic, Transport properties of H-N$_2$ mixtures, Mol. Phys., 103(14), 1895-1904 (2005).
  • AE, A.S. Dickinson and V. Vesovic, A compact formulation for multi-component transport coefficients in gas mixtures, Chem. Phys., 310, 311-319 (2005).
  • AE and J. Proft, A posteriori discontinuous Galerkin error estimates for transient convection-diffusion equations, Appl. Math. Letters, 18, 833-841 (2005).
  • E. Bongiovanni, AE and N. Glinsky-Olivier, Evaluation of an energy relaxation method for the simulation of unsteady, viscous, real gas flows, Int J. Num. Meth. Fluids, 45, 1025-1046 (2004).
  • M. Braack and AE, Coupling multimodeling with local mesh refinement for the numerical computation of laminar flames, Combust. Theory Model., 8(4), 771-788 (2004).
  • E. Burman and AE, Discrete maximum principle for Galerkin approximations of the Laplace operator on arbitrary meshes, C. R. Math. Acad. Sci. Paris, 338, 641-646 (2004).
  • E. Burman, AE and V. Giovangigli, Bunsen flame simulation by finite elements on adaptively refined, unstructured triangulations, Combust. Theory Model., 8(1), 65-84 (2004).
  • L. El Alaoui and AE, Residual and hierarchical a posteriori error estimates for nonconforming mixed finite element methods, ESAIM Math. Mod. Numer. Anal., 38(6), 903-929 (2004).
  • AE, A.S. Dickinson and V. Vesovic, On the behavior of the volume viscosity of atom-molecule mixtures, J. Chem. Phys., 121(17), 8658-8660 (2004).
  • AE and J.-L. Guermond, Accurate numerical simulation of radiative heat transfer with application to crystal growth, Int. J. Num. Meth. Eng., 61, 559-583 (2004).
  • AE, S. Villeneuve and A. Zanette, Adaptive finite element methods for local volatility European option pricing, Int. J. Theor. Appl. Finance, 7(6), 659-684 (2004).
  • E. Bongiovanni, AE and N. Glinsky-Olivier, Une nouvelle méthode de relaxation pour les équations de Navier-Stokes compressibles, C. R. Math. Acad. Sci. Paris, 336, 283-288 (2003).
  • E. Bongiovanni, AE and N. Glinsky-Olivier, A new relaxation method for the compressible Navier-Stokes equations, Math. Meth. Models Appl. Sci., 13(10), 1379-1396 (2003).
  • M. Braack and AE, A posteriori control of modeling errors and discretization errors, Multiscale Model. Simul., 1(2), 221-238 (2003).
  • E. Burman, AE and V. Giovangigli, An adaptive finite element method with crosswind diffusion for low Mach, steady, laminar combustion, J. Comput. Phys., 188(2), 472-492 (2003).
  • AE and V. Giovangigli, Kinetic theory of reactive gas mixtures with application to combustion, Transp. Theory Stat. Phys., 32(5-7), 657-677 (2003).
  • E. Burman and AE, Nonlinear diffusion and discrete maximum principle for stabilized Galerkin approximations of the convection-diffusion-reaction equation, Comp. Meth. Appl. Mech. Eng., 191, 3833-3855 (2002).
  • J. de Charentenay and AE, Multicomponent transport impact on turbulent premixed H$_2$/O$_2$ flames, Combust. Theory Model., 6, 439-462 (2002).
  • AE and V. Giovangigli, Comment on ''Different levels of modeling for diffusion phenomena in neutral and ionized gas mixtures'', J. Thermophysics Heat Transfer, AIAA, 14(1), 119-120, (2000).

• 1993-2000
  • AE and V. Giovangigli, Impact of detailed multicomponent transport on planar and counterflow hydrogen/air and methane/air flames, Combust. Sci. and Tech., 149, 157-181 (1999).
  • AE, J.-L. Guermond, and L. Quartapelle, Vorticity-velocity formulations of the Stokes problem in 3D, Math. Meth. Appl. Sci., 22, 531-546 (1999).
  • AE, Vorticity-velocity formulation of the Stokes problem with variable density and viscosity, Math. Meth. Models Appl. Sci., 8, 203-218 (1998).
  • AE and V. Giovangigli, The kinetic chemical equilibrium regime, Physica A, 260, 49-72 (1998).
  • AE and V. Giovangigli, Thermal diffusion effects in hydrogen/air and methane/air flames, Combust. Theory Model., 2, 349-372 (1998).
  • C.C. Douglas, AE, and M.D. Smooke, Numerical solution of flame sheet problems on serial and parallel computers, Parallel Alg. Appl., 10, 225-236 (1997).
  • AE, Detailed modeling and sensitivity analysis of a rotating disk MOCVD reactor, J. Chem. Vapor Depos., 5, 237-266 (1997).
  • AE and V. Giovangigli, Projected iterative algorithms with application to multicomponent transport, Linear Algebra Appl., 250, 289-315 (1997).
  • AE, V. Giovangigli, and M.D. Smooke, Detailed modeling of three-dimensional chemical vapor deposition, J. Crystal Growth, 180, 670-679 (1997).
  • AE, Vorticity-velocity formulation of the Stokes problem with variable density and viscosity, C. R. Math. Acad. Sci. Paris, 323, 1159-1164 (1996).
  • AE, Sur la formulation tourbillon-vitesse des équations de Navier-Stokes avec densité et viscosité variables, C. R. Acad. Sci. Paris, Sér. IIb, 323, 813-818 (1996).
  • AE and V. Giovangigli, The structure of transport linear systems in dilute isotropic gas mixtures, Phys. Rev. E, 53, 485-492 (1996).
  • AE and V. Giovangigli, Kinetic theory of dilute gas mixtures with independent internal energy modes near equilibrium, Physica A, 224, 613-625 (1996).
  • AE and V. Giovangigli, Optimized transport algorithms for flame codes, Combust. Sci. and Tech., 118, 387-395 (1996).
  • AE, V. Giovangigli, and M.D. Smooke, Numerical study of a three-dimensional chemical vapor deposition reactor with detailed chemistry, J. Comput. Phys., 126, 21-39 (1996).
  • AE, C.C. Douglas, and M.D. Smooke, Detailed chemistry modeling of laminar diffusion flames on parallel computers, Int. J. Supercomput. Appl., 9, 167-186 (1995).
  • AE and V. Giovangigli, Thermal conduction and thermal diffusion in dilute polyatomic gas mixtures, Physica A, 214, 526-546 (1995).
  • AE and V. Giovangigli, Fast and accurate multicomponent transport property evaluation, J. Comput. Phys., 120, 105-116 (1995).
  • AE and V. Giovangigli, Volume viscosity of dilute polyatomic gas mixtures, European J. Mech., B/Fluids, 14, 653-669 (1995).
  • AE and V. Giovangigli, On the evaluation of thermal diffusion coefficients in chemical vapor deposition processes, J. Chem. Vapor Depos., 3, 3-31 (1995).
  • C.C. Douglas, AE, and M.D. Smooke, Parallelizing the numerical solution of laminar diffusion flames, SIAM Newsjournal, 27 (1994).
  • AE, V. Giovangigli, D.E. Keyes, and M.D. Smooke, Towards polyalgorithmic linear system solvers for nonlinear elliptic systems, SIAM J. Sci. Comput., 15, 681-703 (1994).
  • AE and M.D. Smooke, Vorticity-velocity formulation for three-dimensional steady compressible flows, J. Comput. Phys., 105, 58-71 (1993).