Bibliography

Major publications by the team in recent years

• 1S. Boldo, F. Clément, J.-C. Filliâtre, M. Mayero, G. Melquiond, P. Weis.
  
  Wave equation numerical resolution: a comprehensive mechanized proof of a C program, in: Journal of Automated Reasoning, April 2013, vol. 50, n^o 4, pp. 423–456.
  
  http://dx.doi.org/10.1007/s10817-012-9255-4
• 2S. Boldo, F. Clément, J.-C. Filliâtre, M. Mayero, G. Melquiond, P. Weis.
  
  Trusting computations: A mechanized proof from partial differential equations to actual program, in: Computers and Mathematics with Applications, August 2014, vol. 68, n^o 3, pp. 325–352.
  
  http://dx.doi.org/10.1016/j.camwa.2014.06.004
• 3A. Ern, M. Vohralík.
  
  Adaptive inexact Newton methods with a posteriori stopping criteria for nonlinear diffusion PDEs, in: SIAM J. Sci. Comput., 2013, vol. 35, n^o 4, pp. A1761–A1791.
  
  http://dx.doi.org/10.1137/120896918
• 4A. Ern, M. Vohralík.
  
  Polynomial-degree-robust a posteriori estimates in a unified setting for conforming, nonconforming, discontinuous Galerkin, and mixed discretizations, in: SIAM J. Numer. Anal., 2015, vol. 53, n^o 2, pp. 1058–1081.
  
  http://dx.doi.org/10.1137/130950100
• 5T.-T.-P. Hoang, J. Jaffré, C. Japhet, M. Kern, J. E. Roberts.
  
  Space-time domain decomposition methods for diffusion problems in mixed formulations, in: SIAM J. Numer. Anal., 2013, vol. 51, n^o 6, pp. 3532–3559.
  
  http://dx.doi.org/10.1137/130914401
• 6T.-T.-P. Hoang, C. Japhet, M. Kern, J. E. Roberts.
  
  Space-time domain decomposition for reduced fracture models in mixed formulation, in: SIAM J. Numer. Anal., 2016, vol. 54, n^o 1, pp. 288–316.
  
  http://dx.doi.org/10.1137/15M1009651
• 7A. Lejay, G. Pichot.
  
  Simulating diffusion processes in discontinuous media: a numerical scheme with constant time steps, in: J. Comput. Phys., 2012, vol. 231, n^o 21, pp. 7299–7314.
  
  http://dx.doi.org/10.1016/j.jcp.2012.07.011
• 8G. Pichot, J. Erhel, J.-R. De Dreuzy.
  
  A generalized mixed hybrid mortar method for solving flow in stochastic discrete fracture networks, in: SIAM J. Sci. Comput., 2012, vol. 34, n^o 1, pp. B86–B105.
  
  http://dx.doi.org/10.1137/100804383
• 9I. Smears.
  
  Robust and efficient preconditioners for the discontinuous Galerkin time-stepping method, in: IMA Journal of Numerical Analysis, October 2016. [ DOI : 10.1093/imanum/drw050 ]
  
  https://hal.archives-ouvertes.fr/hal-01357497
• 10M. Vohralík, B. I. Wohlmuth.
  
  Mixed finite element methods: implementation with one unknown per element, local flux expressions, positivity, polygonal meshes, and relations to other methods, in: Math. Models Methods Appl. Sci., 2013, vol. 23, n^o 5, pp. 803–838.
  
  http://www.worldscientific.com/doi/abs/10.1142/S0218202512500613

Publications of the year

Doctoral Dissertations and Habilitation Theses

• 11S. Ali Hassan.
  
  A posteriori error estimates and stopping criteria for solvers using the domain decomposition method and with local time stepping, Paris 6 ; Inria Paris, June 2017.
  
  https://hal.inria.fr/tel-01672497
• 12R. Riedlbeck.
  
  Adaptive algorithms for poro-mechanics and poro-plasticity, Université de Montpellier, November 2017.
  
  https://hal.inria.fr/tel-01676709

Articles in International Peer-Reviewed Journals

• 13M. Abbas, A. Ern, N. Pignet.
  
  Hybrid High-Order methods for finite deformations of hyperelastic materials, in: Computational Mechanics, 2018, pp. 1-29, forthcoming.
  
  https://hal.archives-ouvertes.fr/hal-01575370
• 14H. Ben Ameur, G. Chavent, F. Cheikh, F. Clément, V. Martin, J. E. Roberts.
  
  First-Order Indicators for the Estimation of Discrete Fractures in Porous Media, in: Inverse Problems in Science and Engineering, March 2017, 31 p, https://arxiv.org/abs/1602.08304. [ DOI : 10.1080/17415977.2017.1290087 ]
  
  https://hal.inria.fr/hal-01279503
• 15S. Bliudze, S. Furic, J. Sifakis, A. Viel.
  
  Rigorous Design of Cyber-Physical Systems: Linking Physicality and Computation, in: Software and Systems Modeling, 2017, pp. 1-24, forthcoming. [ DOI : 10.1007/s10270-017-0642-5 ]
  
  https://hal.inria.fr/hal-01636392
• 16E. Burman, A. Ern.
  
  A nonlinear consistent penalty method weakly enforcing positivity in the finite element approximation of the transport equation, in: Computer Methods in Applied Mechanics and Engineering, 2017, vol. 320, pp. 122-132. [ DOI : 10.1016/j.cma.2017.03.019 ]
  
  https://hal.archives-ouvertes.fr/hal-01383295
• 17E. Burman, A. Ern, M. A. Fernández.
  
  Fractional-step methods and finite elements with symmetric stabilization for the transient Oseen problem, in: ESAIM: Mathematical Modelling and Numerical Analysis, March 2017, vol. 51, n^o 2, pp. 487-507. [ DOI : 10.1051/m2an/2016028 ]
  
  https://hal.inria.fr/hal-01218328
• 18E. Cancès, G. Dusson, Y. Maday, B. Stamm, M. Vohralík.
  
  Guaranteed and robust a posteriori bounds for Laplace eigenvalues and eigenvectors: conforming approximations, in: SIAM Journal on Numerical Analysis, September 2017, vol. 55, n^o 5, pp. 2228-2254. [ DOI : 10.1137/15M1038633 ]
  
  https://hal.inria.fr/hal-01194364
• 19P. Cantin, A. Ern.
  
  An edge-based scheme on polyhedral meshes for vector advection-reaction equations, in: ESAIM: Mathematical Modelling and Numerical Analysis, 2017. [ DOI : 10.1051/m2an/2016075 ]
  
  https://hal.archives-ouvertes.fr/hal-01324545
• 20D. A. Di Pietro, A. Ern.
  
  Arbitrary-order mixed methods for heterogeneous anisotropic diffusion on general meshes, in: IMA Journal of Numerical Analysis, January 2017, vol. 37, n^o 1, pp. 40-63.
  
  https://hal.archives-ouvertes.fr/hal-00918482
• 21A. Ern, J.-L. Guermond.
  
  Finite element quasi-interpolation and best approximation , in: ESAIM: Mathematical Modelling and Numerical Analysis, 2017. [ DOI : 10.1051/m2an/2016066 ]
  
  https://hal.archives-ouvertes.fr/hal-01155412
• 22A. Ern, I. Smears, M. Vohralík.
  
  Discrete $p$-robust H(div)-liftings and a posteriori estimates for elliptic problems with $H^{-1}$ source terms, in: Calcolo, January 2017, vol. 54, n^o 3, pp. 1009-1025. [ DOI : 10.1007/s10092-017-0217-4 ]
  
  https://hal.inria.fr/hal-01377007
• 23A. Ern, I. Smears, M. Vohralík.
  
  Guaranteed, locally space-time efficient, and polynomial-degree robust a posteriori error estimates for high-order discretizations of parabolic problems, in: SIAM Journal on Numerical Analysis, November 2017, vol. 55, n^o 6, pp. 2811-2834. [ DOI : 10.1137/16M1097626 ]
  
  https://hal.archives-ouvertes.fr/hal-01377086
• 24C. Lusso, F. Bouchut, A. Ern, 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, in: Applied Sciences, April 2017, vol. 7, n^o 4, 386 p. [ DOI : 10.3390/app7040386 ]
  
  https://hal-upec-upem.archives-ouvertes.fr/hal-00992309
• 25C. Lusso, A. Ern, F. Bouchut, A. Mangeney, M. Farin, O. Roche.
  
  Two-dimensional simulation by regularization of free surface viscoplastic flows with Drucker-Prager yield stress and application to granular collapse, in: Journal of Computational Physics, March 2017, vol. 333, pp. 387-408. [ DOI : 10.1016/j.jcp.2016.12.036 ]
  
  https://hal-upec-upem.archives-ouvertes.fr/hal-01133786
• 26J. Papež, Z. Strakoš, M. Vohralík.
  
  Estimating and localizing the algebraic and total numerical errors using flux reconstructions, in: Numerische Mathematik, September 2017. [ DOI : 10.1007/s00211-017-0915-5 ]
  
  https://hal.inria.fr/hal-01312430
• 27J. Ridoux, N. Lardjane, L. Monasse, F. Coulouvrat.
  
  Comparison of Geometrical Shock Dynamics and Kinematic models for shock wave propagation, in: Shock Waves, 2017, forthcoming.
  
  https://hal.archives-ouvertes.fr/hal-01511489
• 28R. Riedlbeck, D. DI PIETRO, A. Ern, S. Granet, K. Kazymyrenko.
  
  Stress and flux reconstruction in Biot's poro-elasticity problem with application to a posteriori error analysis, in: Computers and Mathematics with Applications, April 2017, vol. 73, n^o 7, pp. 1593–1610. [ DOI : 10.1016/j.camwa.2017.02.005 ]
  
  https://hal.archives-ouvertes.fr/hal-01366646
• 29I. Smears.
  
  Nonoverlapping domain decomposition preconditioners for discontinuous Galerkin approximations of Hamilton–Jacobi–Bellman equations, in: Journal of Scientific Computing, 2017. [ DOI : 10.1007/s10915-017-0428-5 ]
  
  https://hal.inria.fr/hal-01428790
• 30M. Vohralík, S. Yousef.
  
  A simple a posteriori estimate on general polytopal meshes with applications to complex porous media flows, in: Computer Methods in Applied Mechanics and Engineering, December 2017. [ DOI : 10.1016/j.cma.2017.11.027 ]
  
  https://hal.archives-ouvertes.fr/hal-01532195
• 31M. Čermák, F. Hecht, Z. Tang, M. Vohralík.
  
  Adaptive inexact iterative algorithms based on polynomial-degree-robust a posteriori estimates for the Stokes problem, in: Numerische Mathematik, November 2017. [ DOI : 10.1007/s00211-017-0925-3 ]
  
  https://hal.inria.fr/hal-01097662

International Conferences with Proceedings

• 32S. Boldo, F. Clément, F. Faissole, V. Martin, M. Mayero.
  
  A Coq Formal Proof of the Lax–Milgram theorem, in: 6th ACM SIGPLAN Conference on Certified Programs and Proofs, Paris, France, January 2017. [ DOI : 10.1145/3018610.3018625 ]
  
  https://hal.inria.fr/hal-01391578
• 33P. Laug, G. Pichot, J.-R. d. Dreuzy.
  
  Realistic geometric modeling of fracture networks, in: 8th International Conference on Adaptive Modeling and Simulation (ADMOS 2017) - Symposium "Mesh generation and mesh adaptativity: methods and applications", Verbania, Italy, June 2017.
  
  https://hal.inria.fr/hal-01591579

National Conferences with Proceedings

• 34S. Boldo, F. Clément, F. Faissole, V. Martin, M. Mayero.
  
  Preuve formelle du théorème de Lax–Milgram, in: 16èmes journées Approches Formelles dans l'Assistance au Développement de Logiciels, Montpellier, France, June 2017.
  
  https://hal.archives-ouvertes.fr/hal-01581807

Conferences without Proceedings

• 35H. Barucq, H. Calandra, G. Chavent, M. V. de Hoop, F. Faucher.
  
  Stability and convergence analysis for seismic depth imaging using FWI, in: Computational Inverse Problems for Partial Differential Equations Workshop, Oberwolfach, Germany, May 2017.
  
  https://hal.archives-ouvertes.fr/hal-01623952
• 36H. Barucq, H. Calandra, G. Chavent, M. V. de Hoop, F. Faucher.
  
  Stability and convergence for seismic reconstruction using full waveform inversion, in: Group Seminar, Linz, Austria, July 2017.
  
  https://hal.archives-ouvertes.fr/hal-01623950
• 37H. Barucq, H. Calandra, G. Chavent, F. Faucher.
  
  Convergence Analysis for Seismic Full Waveform Inversion, in: MATHIAS – TOTAL Symposium on Mathematics, Paris, France, October 2017.
  
  https://hal.archives-ouvertes.fr/hal-01623953
• 38H. Barucq, H. Calandra, G. Chavent, F. Faucher.
  
  Convergence of seismic full waveform inversion and extension to Cauchy data, in: Inverse Days 2017, Oulu, Finland, December 2017.
  
  https://hal.archives-ouvertes.fr/hal-01662677
• 39M. Chavent, G. Chavent.
  
  Approche bloc en ACP group-sparse: le package sparsePCA, in: AngletR 2017 - 6ème Rencontres R, Anglet, France, June 2017, 1 p.
  
  https://hal.archives-ouvertes.fr/hal-01662652
• 40M. Cicuttin, A. Ern, S. Lemaire.
  
  On the implementation of the multiscale Hybrid High-Order method, in: ENUMATH 2017 - European Conference on Numerical Mathematics and Advanced Applications, Voss, Norway, September 2017, pp. 1-8.
  
  https://hal.archives-ouvertes.fr/hal-01661925

Scientific Books (or Scientific Book chapters)

• 41R. Riedlbeck, D. A. Di Pietro, A. Ern.
  
  Equilibrated stress reconstructions for linear elasticity problems with application to a posteriori error analysis, in: Finite Volumes for Complex Applications VIII – Methods and Theoretical Aspects, June 2017. [ DOI : 10.1007/978-3-319-57397-7 ]
  
  https://hal.archives-ouvertes.fr/hal-01433841

Scientific Popularization

• 42F. Clément.
  
  Les mathématiques s’appliquent aussi à l’industrie, in: Interstices, January 2017.
  
  https://hal.inria.fr/hal-01466798

Other Publications

• 43E. Ahmed, S. Ali Hassan, C. Japhet, M. Kern, M. Vohralík.
  
  A posteriori error estimates and stopping criteria for space-time domain decomposition for two-phase flow between different rock types, June 2017, working paper or preprint.
  
  https://hal.inria.fr/hal-01540956
• 44E. Ahmed, A. Ben Abda.
  
  The sub-Cauchy Stokes Problem: Solvability Issues and Lagrange Multiplier Methods with Artificial Boundary Conditions, October 2017, working paper or preprint.
  
  https://hal.archives-ouvertes.fr/hal-01467425
• 45S. Ali Hassan, C. Japhet, M. Kern, M. Vohralík.
  
  A posteriori stopping criteria for optimized Schwarz domain decomposition algorithms in mixed formulations, May 2017, working paper or preprint.
  
  https://hal.inria.fr/hal-01529532
• 46S. Ali Hassan, C. Japhet, M. Vohralík.
  
  A posteriori stopping criteria for space-time domain decomposition for the heat equation in mixed formulations , September 2017, working paper or preprint.
  
  https://hal.inria.fr/hal-01586862
• 47L. Amir, M. Kern.
  
  Preconditioning a coupled model for reactive transport in porous media, September 2017, https://arxiv.org/abs/1710.01483 - working paper or preprint.
  
  https://hal.inria.fr/hal-01327307
• 48A. BENACEUR, V. Ehrlacher, A. Ern, S. Meunier.
  
  A progressive reduced basis/empirical interpolation method for nonlinear parabolic problems , November 2017, working paper or preprint.
  
  https://hal.archives-ouvertes.fr/hal-01599304
• 49T. Boiveau, V. Ehrlacher, A. Ern, A. Nouy.
  
  Low-rank approximation of linear parabolic equations by space-time tensor Galerkin methods, December 2017, working paper or preprint.
  
  https://hal.archives-ouvertes.fr/hal-01668316
• 50E. Burman, A. Ern.
  
  A cut-cell Hybrid High-Order method for elliptic problems with curved boundaries, December 2017, working paper or preprint.
  
  https://hal.archives-ouvertes.fr/hal-01653685
• 51E. Burman, A. Ern.
  
  An unfitted Hybrid High-Order method for elliptic interface problems *, October 2017, working paper or preprint.
  
  https://hal.archives-ouvertes.fr/hal-01625421
• 52V. M. Calo, M. Cicuttin, Q. Deng, A. Ern.
  
  Spectral approximation of elliptic operators by the Hybrid High-Order method, November 2017, working paper or preprint.
  
  https://hal.archives-ouvertes.fr/hal-01628698
• 53E. Cancès, G. Dusson, Y. Maday, B. Stamm, M. Vohralík.
  
  Guaranteed and robust a posteriori bounds for Laplace eigenvalues and eigenvectors: a unified framework, March 2017, working paper or preprint.
  
  https://hal.inria.fr/hal-01483461
• 54M. Chavent, G. Chavent.
  
  Group-sparse block PCA and explained variance, December 2017, https://arxiv.org/abs/1705.00461 - working paper or preprint.
  
  https://hal.archives-ouvertes.fr/hal-01662605
• 55P. Ciarlet, M. Vohralík.
  
  Localization of global norms and robust a posteriori error control for transmission problems with sign-changing coefficients, August 2017, working paper or preprint.
  
  https://hal.inria.fr/hal-01148476
• 56M. Cicuttin, D. A. Di Pietro, A. Ern.
  
  Implementation of Discontinuous Skeletal methods on arbitrary-dimensional, polytopal meshes using generic programming, September 2017, working paper or preprint.
  
  https://hal.archives-ouvertes.fr/hal-01429292
• 57M. Cicuttin, A. Ern, S. Lemaire.
  
  A Multiscale Hybrid High-Order method, February 2017, working paper or preprint.
  
  https://hal.archives-ouvertes.fr/hal-01467434
• 58J. Dabaghi, V. Martin, M. Vohralík.
  
  Adaptive inexact semismooth Newton methods for the contact problem between two membranes, December 2017, working paper or preprint.
  
  https://hal.inria.fr/hal-01666845
• 59P. Daniel, A. Ern, I. Smears, M. Vohralík.
  
  An adaptive $hp$-refinement strategy with computable guaranteed bound on the error reduction factor, December 2017, working paper or preprint.
  
  https://hal.inria.fr/hal-01666763
• 60A. Ern, J.-L. Guermond.
  
  Abstract nonconforming error estimates and application to boundary penalty methods for diffusion equations and time-harmonic Maxwell's equations, November 2017, working paper or preprint.
  
  https://hal.archives-ouvertes.fr/hal-01563594
• 61A. Ern, J.-L. Guermond.
  
  Analysis of the edge finite element approximation of the Maxwell equations with low regularity solutions, June 2017, working paper or preprint.
  
  https://hal.archives-ouvertes.fr/hal-01531940
• 62A. Ern, I. Smears, M. Vohralík.
  
  Equilibrated flux a posteriori error estimates in $L^2\left(H^1\right)$-norms for high-order discretizations of parabolic problems, March 2017, working paper or preprint.
  
  https://hal.inria.fr/hal-01489721
• 63M. Jensen, I. Smears.
  
  On the notion of boundary conditions in comparison principles for viscosity solutions, March 2017, working paper or preprint.
  
  https://hal.inria.fr/hal-01493586
• 64A. Lejay, L. Lenôtre, G. Pichot.
  
  Analytic expressions of the solutions of advection-diffusion problems in 1D with discontinuous coefficients, November 2017, working paper or preprint.
  
  https://hal.inria.fr/hal-01644270
• 65F. Marazzato, A. Ern, C. Mariotti, L. Monasse.
  
  An explicit energy-momentum conserving time-integration scheme for Hamiltonian dynamics, December 2017, working paper or preprint.
  
  https://hal-enpc.archives-ouvertes.fr/hal-01661608
• 66J. Papež, U. Rüde, M. Vohralík, B. Wohlmuth.
  
  Sharp algebraic and total a posteriori error bounds for $h$ and $p$ finite elements via a multilevel approach, December 2017, working paper or preprint.
  
  https://hal.inria.fr/hal-01662944
• 67M. Riahi, H. Ben Ameur, J. Jaffré, R. Bouhlila.
  
  Refinement indicators for estimating hydrogeologic parameters, January 2018, working paper or preprint.
  
  https://hal.inria.fr/hal-01674486