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]

  • E. Burman, G. Delay and AE, The unique continuation problem for the wave equation discretized with a high-order space-time nonconforming method [hal]

  • E. Burman, AE and J. Preuss, A hybridized Nitsche method for sign-changing elliptic PDEs [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, A priori and a posteriori analysis of the discontinuous Galerkin approximation of the time-harmonic Maxwell's equations under minimal regularity assumptions [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]

  • Z. Dong and AE, hp-error analysis of mixed-order hybrid high-order methods for elliptic problems on simplicial meshes [hal] [arXiv]

  • 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 and R. Khot, Explicit Runge--Kutta schemes with hybrid high-order methods for the wave equation in first-order form [hal]

  • A. Kabalan, F. Casenave, F. Bordeu, V. Ehrlacher and AE, Elasticity-based mesh morphing technique and application to reduced-order modeling [hal] [arXiv]

• 2024

  • Z. Dong and AE, C⁰-hybrid high-order methods for biharmonic problems, IMA J. Numer. Anal., 44(1), 24-57 (2024) [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, SIAM J. Numer. Anal. to appear (2024) [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, J. Sci. Comput., 100(3), Paper No. 83, 30 pp. (2024) [hal] [Springer link]

  • 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, J. Sci. Comput., 101(1), Paper No. 7, 28 pp. (2024) [hal] [Springer link]

  • I. Niakh, G. Drouet, V. Ehrlacher, and AE, A reduced basis method for frictional contact problems formulated with Nitsche's method, SMAI J. Comput. Math., 10, 29-54 (2024) [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] [pdf, copyright SIAM]

  • 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] [pdf, copyright EDP Sciences and SMAI]

  • 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] [pdf, copyright SMAI]

  • 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] Frontiers of Science Award, Int. Congress Basic Science, Beijing, 2024

  • 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]

  • AE, 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).