Team, Visitors, External Collaborators
Overall Objectives
Research Program
Application Domains
Highlights of the Year
New Software and Platforms
New Results
Bilateral Contracts and Grants with Industry
Partnerships and Cooperations
Dissemination
Bibliography
XML PDF e-pub
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Bibliography

Major publications by the team in recent years
[1]
S. Boldo, F. Cl√©ment, J.-C. Filli√Ętre, 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, no¬†4, pp. 423‚Äď456.
http://dx.doi.org/10.1007/s10817-012-9255-4
[2]
S. Boldo, F. Cl√©ment, J.-C. Filli√Ętre, 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, no¬†3, pp. 325‚Äď352.
http://dx.doi.org/10.1016/j.camwa.2014.06.004
[3]
E. 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, no¬†5, pp. 2228‚Äď2254.
http://dx.doi.org/10.1137/15M1038633
[4]
D. 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‚Äď21.
http://dx.doi.org/10.1016/j.cma.2014.09.009
[5]
A. Ern, J.-L. Guermond.
Finite element quasi-interpolation and best approximation, in: ESAIM Math. Model. Numer. Anal., 2017, vol.¬†51, no¬†4, pp. 1367‚Äď1385.
https://doi.org/10.1051/m2an/2016066
[6]
A. 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, no¬†2, pp. 1058‚Äď1081.
http://dx.doi.org/10.1137/130950100
[7]
T.-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, no¬†6, pp. 3532‚Äď3559.
http://dx.doi.org/10.1137/130914401
[8]
T.-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, no¬†1, pp. 288‚Äď316.
http://dx.doi.org/10.1137/15M1009651
[9]
A. Lejay, G. Pichot.
Simulating diffusion processes in discontinuous media: a numerical scheme with constant time steps, in: J. Comput. Phys., 2012, vol.¬†231, no¬†21, pp. 7299‚Äď7314.
http://dx.doi.org/10.1016/j.jcp.2012.07.011
[10]
G. 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, no¬†1, pp. B86‚ÄďB105.
http://dx.doi.org/10.1137/100804383
Publications of the year

Doctoral Dissertations and Habilitation Theses

[11]
J. 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
[12]
P. 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
[13]
N. 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

[14]
M. 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
[15]
M. 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
[16]
E. 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
[17]
L. Amir, M. Kern.
Preconditioning a coupled model for reactive transport in porous media, in: International Journal of Numerical Analysis and Modeling, 2019, vol. 16, no 1, pp. 18-48, https://arxiv.org/abs/1710.01483.
https://hal.inria.fr/hal-01327307
[18]
H. 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
[19]
I. 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
[20]
A. 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
[21]
J. 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
[22]
S. 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, no¬†3, pp. 1613‚Äď1636, forthcoming. [ DOI : 10.1007/s10270-017-0642-5 ]
https://hal.inria.fr/hal-01636392
[23]
T. 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, no 2, pp. 635-658, https://arxiv.org/abs/1712.07256. [ DOI : 10.1051/m2an/2018073 ]
https://hal.archives-ouvertes.fr/hal-01668316
[24]
V. 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, no 318, pp. 1559-1586.
https://hal.archives-ouvertes.fr/hal-01628698
[25]
M. Cicuttin, A. Ern, S. Lemaire.
A Hybrid High-Order method for highly oscillatory elliptic problems, in: Computational Methods in Applied Mathematics, 2019, vol. 19, no 4, pp. 723-748. [ DOI : 10.1515/cmam-2018-0013 ]
https://hal.archives-ouvertes.fr/hal-01467434
[26]
P. 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
[27]
A. Ern, I. Smears, M. Vohralík.
Equilibrated flux a posteriori error estimates in L2(H1)-norms for high-order discretizations of parabolic problems, in: IMA Journal of Numerical Analysis, 2019, vol. 39, no 3, pp. 1158-1179. [ DOI : 10.1093/imanum/dry035 ]
https://hal.inria.fr/hal-01489721
[28]
A. 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
[29]
A. Lejay, L. Len√ītre, 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
[30]
A. Lejay, L. Len√ītre, 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, no 5, pp. 1823-1849. [ DOI : 10.1137/18M1164500 ]
https://hal.inria.fr/hal-01644270
[31]
G. 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
[32]
F. 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

[33]
E. 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
[34]
T. 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
[35]
M. 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
[36]
F. 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

[37]
H. 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, no RR-9253, Material under review by journal Geophysics.
https://hal.archives-ouvertes.fr/hal-02016373

Other Publications

[38]
E. 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
[39]
A. Benaceur.
A time-dependent Parametrized Background Data-Weak approach, October 2019, working paper or preprint.
https://hal.archives-ouvertes.fr/hal-02330408
[40]
A. 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
[41]
E. 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
[42]
E. 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
[43]
V. 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
[44]
E. 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
[45]
E. 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
[46]
C. 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
[47]
J.-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
[48]
T. 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
[49]
F. 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
[50]
M. 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
[51]
J. 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
[52]
J. 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
[53]
A. 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
[54]
A. Ern, M. Vohralík, M. Zakerzadeh.
Guaranteed and robust L2-norm a posteriori error estimates for 1D linear advection problems, April 2019, working paper or preprint.
https://hal.archives-ouvertes.fr/hal-02105418
[55]
A. Ern, P. Zanotti.
A quasi-optimal variant of the hybrid high-order method for elliptic PDEs with H‚ąí1 loads, April 2019, working paper or preprint.
https://hal.archives-ouvertes.fr/hal-02114715
[56]
F. 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
[57]
R. 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
[58]
A. Mira√ßi, J. PapeŇĺ, M. Vohral√≠k.
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
[59]
J. PapeŇĺ, U. R√ľde, M. Vohral√≠k, 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
[60]
J. PapeŇĺ, M. Vohral√≠k.
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