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
• 3E. Cancès, G. Dusson, Y. Maday, B. Stamm, M. Vohralík.
  Guaranteed and robust a posteriori bounds for Laplace eigenvalues and eigenvectors: conforming approximations, in: SIAM J. Numer. Anal., 2017, vol. 55, n^o 5, pp. 2228–2254.
  http://dx.doi.org/10.1137/15M1038633
• 4D. A. Di Pietro, A. Ern.
  A hybrid high-order locking-free method for linear elasticity on general meshes, in: Comput. Methods Appl. Mech. Engrg., 2015, vol. 283, pp. 1–21.
  http://dx.doi.org/10.1016/j.cma.2014.09.009
• 5A. Ern, J.-L. Guermond.
  Finite element quasi-interpolation and best approximation, in: ESAIM Math. Model. Numer. Anal., 2017, vol. 51, n^o 4, pp. 1367–1385.
  https://doi.org/10.1051/m2an/2016066
• 6A. 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
• 7T.-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
• 8T.-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
• 9A. 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
• 10G. 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

Publications of the year

Doctoral Dissertations and Habilitation Theses

• 11J. Dabaghi.
  A posteriori error estimates for variational inequalities: application to a two-phase flow in porous media, Sorbonne Université, Université Pierre et Marie Curie, Paris 6, June 2019.
  https://hal.archives-ouvertes.fr/tel-02151951
• 12P. Daniel.
  Adaptive hp-finite elements with guaranteed error contraction and inexact multilevel solvers, Sorbonne Université ; Inria Paris, March 2019.
  https://hal.inria.fr/tel-02104982
• 13N. Pignet.
  Hybrid High-Order methods for nonlinear solid mechanics, Université Paris-Est Marne la Vallée, October 2019.
  https://tel.archives-ouvertes.fr/tel-02318157

Articles in International Peer-Reviewed Journals

• 14M. Abbas, A. Ern, N. Pignet.
  A Hybrid High-Order method for finite elastoplastic deformations within a logarithmic strain framework, in: International Journal for Numerical Methods in Engineering, June 2019. [ DOI : 10.1002/nme.6137 ]
  https://hal.archives-ouvertes.fr/hal-01978385
• 15M. Abbas, A. Ern, N. Pignet.
  A Hybrid High-Order method for incremental associative plasticity with small deformations, in: Computer Methods in Applied Mechanics and Engineering, April 2019, vol. 346, pp. 891-912, https://arxiv.org/abs/1804.06129. [ DOI : 10.1016/j.cma.2018.08.037 ]
  https://hal.archives-ouvertes.fr/hal-01768411
• 16E. 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, in: SMAI Journal of Computational Mathematics, December 2019, vol. 5, pp. 195-227.
  https://hal.inria.fr/hal-01540956
• 17L. Amir, M. Kern.
  Preconditioning a coupled model for reactive transport in porous media, in: International Journal of Numerical Analysis and Modeling, 2019, vol. 16, n^o 1, pp. 18-48, https://arxiv.org/abs/1710.01483.
  https://hal.inria.fr/hal-01327307
• 18H. Barucq, G. Chavent, F. Faucher.
  A priori estimates of attraction basins for nonlinear least squares, with application to Helmholtz seismic inverse problem, in: Inverse Problems, 2019, forthcoming. [ DOI : 10.1088/1361-6420/ab3507 ]
  https://hal.archives-ouvertes.fr/hal-02194212
• 19I. Ben Gharbia, J. Dabaghi, V. Martin, M. Vohralík.
  A posteriori error estimates and adaptive stopping criteria for a compositional two-phase flow with nonlinear complementarity constraints, in: Computational Geosciences, December 2019. [ DOI : 10.1007/s10596-019-09909-5 ]
  https://hal.archives-ouvertes.fr/hal-01919067
• 20A. Benaceur, A. Ern, V. Ehrlacher.
  A reduced basis method for parametrized variational inequalities applied to contact mechanics, in: International Journal for Numerical Methods in Engineering, October 2019. [ DOI : 10.1002/nme.6261 ]
  https://hal.archives-ouvertes.fr/hal-02081485
• 21J. Blechta, J. Málek, M. Vohralík.
  Localization of the $W^{-1,q}$ norm for local a posteriori efficiency, in: IMA Journal of Numerical Analysis, March 2019. [ DOI : 10.1093/imanum/drz002 ]
  https://hal.inria.fr/hal-01332481
• 22S. Bliudze, S. Furic, J. Sifakis, A. Viel.
  Rigorous Design of Cyber-Physical Systems : Linking Physicality and Computation, in: Software and Systems Modeling, 2019, vol. 18, n^o 3, pp. 1613–1636, forthcoming. [ DOI : 10.1007/s10270-017-0642-5 ]
  https://hal.inria.fr/hal-01636392
• 23T. Boiveau, V. Ehrlacher, A. Ern, A. Nouy.
  Low-rank approximation of linear parabolic equations by space-time tensor Galerkin methods, in: ESAIM: Mathematical Modelling and Numerical Analysis, May 2019, vol. 53, n^o 2, pp. 635-658, https://arxiv.org/abs/1712.07256. [ DOI : 10.1051/m2an/2018073 ]
  https://hal.archives-ouvertes.fr/hal-01668316
• 24V. M. Calo, M. Cicuttin, Q. Deng, A. Ern.
  Spectral approximation of elliptic operators by the Hybrid High-Order method, in: Mathematics of Computation, 2019, vol. 88, n^o 318, pp. 1559-1586.
  https://hal.archives-ouvertes.fr/hal-01628698
• 25M. Cicuttin, A. Ern, S. Lemaire.
  A Hybrid High-Order method for highly oscillatory elliptic problems, in: Computational Methods in Applied Mathematics, 2019, vol. 19, n^o 4, pp. 723-748. [ DOI : 10.1515/cmam-2018-0013 ]
  https://hal.archives-ouvertes.fr/hal-01467434
• 26P. Daniel, A. Ern, M. Vohralík.
  An adaptive $hp$-refinement strategy with inexact solvers and computable guaranteed bound on the error reduction factor, in: Computer Methods in Applied Mechanics and Engineering, November 2019, vol. 359, 112607 p. [ DOI : 10.1016/j.cma.2019.112607 ]
  https://hal.inria.fr/hal-01931448
• 27A. 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, in: IMA Journal of Numerical Analysis, 2019, vol. 39, n^o 3, pp. 1158-1179. [ DOI : 10.1093/imanum/dry035 ]
  https://hal.inria.fr/hal-01489721
• 28A. Ern, M. Vohralík.
  Stable broken H1 and H(div) polynomial extensions for polynomial-degree-robust potential and flux reconstruction in three space dimensions, in: Mathematics of Computation, October 2019. [ DOI : 10.1090/mcom/3482 ]
  https://hal.inria.fr/hal-01422204
• 29A. Lejay, L. Lenôtre, G. Pichot.
  An exponential timestepping algorithm for diffusion with discontinuous coefficients, in: Journal of Computational Physics, November 2019, vol. 396, pp. 888-904. [ DOI : 10.1016/j.jcp.2019.07.013 ]
  https://hal.inria.fr/hal-01806465
• 30A. Lejay, L. Lenôtre, G. Pichot.
  Analytic expressions of the solutions of advection-diffusion problems in 1D with discontinuous coefficients, in: SIAM Journal on Applied Mathematics, September 2019, vol. 79, n^o 5, pp. 1823-1849. [ DOI : 10.1137/18M1164500 ]
  https://hal.inria.fr/hal-01644270
• 31G. Mallik, M. Vohralík, S. Yousef.
  Goal-oriented a posteriori error estimation for conforming and nonconforming approximations with inexact solvers, in: Journal of Computational and Applied Mathematics, August 2019, vol. 366, 112367 p. [ DOI : 10.1016/j.cam.2019.112367 ]
  https://hal.inria.fr/hal-01964733
• 32F. Marazzato, A. Ern, C. Mariotti, L. Monasse.
  An explicit pseudo-energy conserving time-integration scheme for Hamiltonian dynamics, in: Computer Methods in Applied Mechanics and Engineering, April 2019, vol. 347, pp. 906-927. [ DOI : 10.1016/j.cma.2019.01.013 ]
  https://hal-enpc.archives-ouvertes.fr/hal-01661608

International Conferences with Proceedings

• 33E. Burman, A. Ern.
  A cut-cell Hybrid High-Order method for elliptic problems with curved boundaries, in: ENUMATH 2017, Bergen, Norway, EnuMath 2019 - European Numerical Mathematics and Advanced Applications Conference, 2019. [ DOI : 10.1007/978-3-319-96415-7_14 ]
  https://hal.archives-ouvertes.fr/hal-01653685
• 34T. Chaumont-Frelet, A. Ern, M. Vohralík.
  Asymptotically constant-free, p-robust and guaranteed a posteriori error estimates for the Helmholtz equation, in: EnuMath 2019 - European Numerical Mathematics and Advanced Applications Conference, Egmond aan Zee, Netherlands, September 2019.
  https://hal.inria.fr/hal-02321140
• 35M. Cicuttin, A. Ern, S. Lemaire.
  On the implementation of a multiscale Hybrid High-Order method, in: ENUMATH 2017, Bergen, Norway, I. Berre, K. Kumar, J. M. Nordbotten, I. S. Pop, F. A. Radu (editors), Numerical Mathematics and Advanced Applications - ENUMATH 2017, Springer, Cham, 2019, vol. 126, pp. 509-517. [ DOI : 10.1007/978-3-319-96415-7_46 ]
  https://hal.archives-ouvertes.fr/hal-01661925
• 36F. Hédin, G. Pichot, A. Ern.
  A hybrid high-order method for flow simulations in discrete fracture networks, in: ENUMATH - European Numerical Mathematics and Advanced Applications Conference 2019, Egmond aan Zee, Netherlands, September 2019.
  https://hal.inria.fr/hal-02315491

Internal Reports

• 37H. Barucq, H. Calandra, G. Chavent, F. Faucher.
  A priori estimates of attraction basins for velocity model reconstruction by time-harmonic Full Waveform Inversion and Data Space Reflectivity formulation, Magique 3D ; Inria Bordeaux Sud-Ouest ; Université de Pau et des Pays de l'Adour, February 2019, n^o RR-9253, Material under review by journal Geophysics.
  https://hal.archives-ouvertes.fr/hal-02016373

Other Publications

• 38E. Ahmed, C. Japhet, M. Kern.
  Space-time domain decomposition for two-phase flow between different rock types, January 2020, working paper or preprint.
  https://hal.inria.fr/hal-02275690
• 39A. Benaceur.
  A time-dependent Parametrized Background Data-Weak approach, October 2019, working paper or preprint.
  https://hal.archives-ouvertes.fr/hal-02330408
• 40A. Benaceur.
  An inexpensive Parametrized Background Data-Weak approach for time-dependent problems, August 2019, working paper or preprint.
  https://hal.archives-ouvertes.fr/hal-02265533
• 41E. Burman, M. Cicuttin, G. Delay, A. Ern.
  An unfitted Hybrid High-Order method with cell agglomeration for elliptic interface problems, September 2019, working paper or preprint.
  https://hal.archives-ouvertes.fr/hal-02280426
• 42E. Burman, G. Delay, A. Ern.
  The unfitted HHO method for the Stokes problem on curved domains, January 2020, working paper or preprint.
  https://hal.archives-ouvertes.fr/hal-02438622
• 43V. M. Calo, A. Ern, I. Muga, S. Rojas.
  An adaptive stabilized conforming finite element method via residual minimization on dual discontinuous Galerkin norms, 2019, https://arxiv.org/abs/1907.12605 - working paper or preprint.
  https://hal.archives-ouvertes.fr/hal-02196242
• 44E. Cancès, G. Dusson, Y. Maday, B. Stamm, M. Vohralík.
  Guaranteed a posteriori bounds for eigenvalues and eigenvectors: multiplicities and clusters, May 2019, working paper or preprint.
  https://hal.archives-ouvertes.fr/hal-02127954
• 45E. Cancès, G. Dusson, Y. Maday, B. Stamm, M. Vohralík.
  Post-processing of the planewave approximation of Schrödinger equations. Part I: linear operators, January 2020, working paper or preprint.
  https://hal.archives-ouvertes.fr/hal-01908039
• 46C. Cancès, F. Nabet, M. Vohralík.
  Convergence and a posteriori error analysis for energy-stable finite element approximations of degenerate parabolic equations, January 2019, working paper or preprint.
  https://hal.archives-ouvertes.fr/hal-01894884
• 47J.-P. Chancelier, S. Furic, P. Weis.
  Translating Simulink Models to Modelica using the Nsp Platform, February 2019, working paper or preprint.
  https://hal.archives-ouvertes.fr/hal-01948681
• 48T. Chaumont-Frelet, A. Ern, M. Vohralík.
  On the derivation of guaranteed and p-robust a posteriori error estimates for the Helmholtz equation, July 2019, working paper or preprint.
  https://hal.inria.fr/hal-02202233
• 49F. Chouly, A. Ern, N. Pignet.
  A Hybrid High-Order discretization combined with Nitsche's method for contact and Tresca friction in small strain elasticity, September 2019, working paper or preprint.
  https://hal.archives-ouvertes.fr/hal-02283418
• 50M. Cicuttin, A. Ern, T. Gudi.
  Hybrid high-order methods for the elliptic obstacle problem, May 2019, working paper or preprint.
  https://hal.archives-ouvertes.fr/hal-01718883
• 51J. Dabaghi, V. Martin, M. Vohralík.
  A posteriori estimates distinguishing the error components and adaptive stopping criteria for numerical approximations of parabolic variational inequalities, August 2019, working paper or preprint.
  https://hal.archives-ouvertes.fr/hal-02274493
• 52J. Erhel, M. Oumouni, G. Pichot, F. Schoefs.
  Analysis of continuous spectral method for sampling stationary Gaussian random fields, April 2019, working paper or preprint.
  https://hal.archives-ouvertes.fr/hal-02109037
• 53A. Ern, T. Gudi, I. Smears, M. Vohralík.
  Equivalence of local-and global-best approximations, a simple stable local commuting projector, and optimal hp approximation estimates in H(div), August 2019, https://arxiv.org/abs/1908.08158 - working paper or preprint.
  https://hal.inria.fr/hal-02268960
• 54A. Ern, M. Vohralík, M. Zakerzadeh.
  Guaranteed and robust $L^2$-norm a posteriori error estimates for 1D linear advection problems, April 2019, working paper or preprint.
  https://hal.archives-ouvertes.fr/hal-02105418
• 55A. Ern, P. Zanotti.
  A quasi-optimal variant of the hybrid high-order method for elliptic PDEs with $H^{-1}$ loads, April 2019, working paper or preprint.
  https://hal.archives-ouvertes.fr/hal-02114715
• 56F. Marazzato, A. Ern, L. Monasse.
  A consistent discrete element method for quasi-static and dynamic elasto-plasticity, November 2019, https://arxiv.org/abs/1911.00738 - working paper or preprint.
  https://hal.archives-ouvertes.fr/hal-02343280
• 57R. Milani, J. Bonelle, A. Ern.
  Compatible Discrete Operator schemes for the steady incompressible Stokes and Navier-Stokes equations, December 2019, working paper or preprint.
  https://hal.archives-ouvertes.fr/hal-02417514
• 58A. Miraçi, J. Papež, M. Vohralík.
  A multilevel algebraic error estimator and the corresponding iterative solver with $p$-robust behavior, July 2019, working paper or preprint.
  https://hal.archives-ouvertes.fr/hal-02070981
• 59J. 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. Recovering mass balance in any situation, December 2019, working paper or preprint.
  https://hal.inria.fr/hal-01662944
• 60J. Papež, M. Vohralík.
  Inexpensive guaranteed and efficient upper bounds on the algebraic error in finite element discretizations, January 2020, working paper or preprint.
  https://hal.inria.fr/hal-02422851