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

• 11N. Birgle.
  
  Underground flow, numerical methods and high performance computing, Université Pierre et Marie Curie - Paris VI, March 2016.
  
  https://tel.archives-ouvertes.fr/tel-01366054
• 12F. Cheikh.
  
  Identification of fractures in porous medium, UPMC - Université Paris 6 Pierre et Marie Curie ; ENIT Tunis, October 2016.
  
  https://hal.inria.fr/tel-01415825
• 13M. H. Riahi.
  
  Identification of hydrogeological parameters in a porous medium, Universite Pierre & Marie Curie, October 2016.
  
  https://hal.inria.fr/tel-01423829

Articles in International Peer-Reviewed Journals

• 14P. F. Antonietti, P. Houston, I. Smears.
  
  A Note on Optimal spectral bounds for nonoverlapping domain decomposition preconditioners for $hp$–Version Discontinuous Galerkin methods, in: International Journal of Numerical Analysis and Modeling, 2016, vol. 13, n^o 4, pp. 513-524.
  
  https://hal.inria.fr/hal-01428749
• 15E. Cancès, G. Dusson, Y. Maday, B. Stamm, M. Vohralík.
  
  A perturbation-method-based post-processing for the planewave discretization of Kohn–Sham models, in: Journal of Computational Physics, February 2016, vol. 307, pp. 446–459. [ DOI : 10.1016/j.jcp.2015.12.012 ]
  
  http://hal.upmc.fr/hal-01140818
• 16V. Dolejší, A. Ern, M. Vohralík.
  
  hp-adaptation driven by polynomial-degree-robust a posteriori error estimates for elliptic problems, in: SIAM Journal on Scientific Computing, October 2016, vol. 38, n^o 5, pp. A3220-A3246.
  
  https://hal.inria.fr/hal-01165187
• 17T.-T.-P. Hoang, C. Japhet, M. Kern, J. E. Roberts.
  
  Space-time Domain Decomposition and Mixed Formulation for solving reduced fracture models, in: SIAM Journal on Numerical Analysis, February 2016, vol. 54, n^o 1, 29 p. [ DOI : 10.1137/15M1009651 ]
  
  https://hal.inria.fr/hal-01113953
• 18C. Josz, D. Henrion.
  
  Strong duality in Lasserre's hierarchy for polynomial optimization, in: Optimization Letters, January 2016, vol. 10, n^o 1, pp. 3-10. [ DOI : 10.1007/s11590-015-0868-5 ]
  
  https://hal.archives-ouvertes.fr/hal-00997726
• 19A. Lejay, G. Pichot.
  
  Simulating Diffusion Processes in Discontinuous Media: Benchmark Tests, in: Journal of Computational Physics, June 2016, vol. 314, pp. 348-413. [ DOI : 10.1016/j.jcp.2016.03.003 ]
  
  https://hal.inria.fr/hal-01003853
• 20I. 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
• 21I. Smears, E. Süli.
  
  Discontinuous Galerkin finite element methods for time-dependent Hamilton-Jacobi-Bellman equations with Cordes coefficients, in: Numerische Mathematik, May 2016, vol. 133, n^o 1, pp. 141 - 176. [ DOI : 10.1007/s00211-015-0741-6 ]
  
  https://hal.inria.fr/hal-01428647

International Conferences with Proceedings

• 22S. 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.
  
  https://hal.inria.fr/hal-01391578
• 23J.-R. De Dreuzy, G. Pichot, P. Laug, J. Erhel.
  
  Flow simulation in 3D Discrete Fracture Networks, in: The XXI International Conference Computational Methods in Water Resources, Toronto, ON, Canada, June 2016.
  
  https://hal.inria.fr/hal-01387391

Scientific Books (or Scientific Book chapters)

• 24M. Kern.
  
  Méthodes numériques pour les problèmes inverses, Collection Mathématiques et statisitques, ISTE Éditions, March 2016, 222 p.
  
  https://hal.inria.fr/hal-01297083

Internal Reports

• 25H. 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, Inria Paris, February 2016, n^o RR-8857, 31 p.
  
  https://hal.inria.fr/hal-01279503
• 26F. Clément, V. Martin.
  
  The Lax-Milgram Theorem. A detailed proof to be formalized in Coq, Inria Paris, July 2016, n^o RR-8934.
  
  https://hal.inria.fr/hal-01344090
• 27G. Pichot.
  
  TECHNICAL REPORT N° 484 Algorithms for Gaussian random field generation, Inria Paris, December 2016, n^o RT-0484.
  
  https://hal.inria.fr/hal-01414707
• 28M. H. Riahi, H. Ben Ameur, J. Jaffré, R. Bouhlila.
  
  Refinement indicators for estimating hydrogeologic parameters, Inria Paris, February 2016, n^o RR-8877, 25 p.
  
  https://hal.inria.fr/hal-01285127

Other Publications

• 29L. Amir, M. Kern.
  
  Preconditioning a coupled model for reactive transport in porous media, June 2016, working paper or preprint.
  
  https://hal.inria.fr/hal-01327307
• 30J. Blechta, J. Málek, M. Vohralík.
  
  Localization of the $W^{-1,q}$ norm for local a posteriori efficiency, June 2016, working paper or preprint.
  
  https://hal.inria.fr/hal-01332481
• 31E. Cancès, G. Dusson, Y. Maday, B. Stamm, M. Vohralík.
  
  Guaranteed and robust a posteriori bounds for Laplace eigenvalues and eigenvectors: conforming approximations, December 2016, working paper or preprint.
  
  https://hal.inria.fr/hal-01194364
• 32A. Ern, I. Smears, M. Vohralík.
  
  Discrete $p$-robust H(div)-liftings and a posteriori estimates for elliptic problems with $H^{-1}$ source terms, October 2016, working paper or preprint.
  
  https://hal.inria.fr/hal-01377007
• 33A. 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, October 2016, working paper or preprint.
  
  https://hal.archives-ouvertes.fr/hal-01377086
• 34A. Ern, M. Vohralík.
  
  Stable broken H1 and H(div) polynomial extensions for polynomial-degree-robust potential and flux reconstruction in three space dimensions, December 2016, working paper or preprint.
  
  https://hal.inria.fr/hal-01422204
• 35T.-T.-P. Hoang, C. Japhet, M. Kern, J. E. Roberts.
  
  Space-time domain decomposition for advection-diffusion problems in mixed formulations, March 2016, working paper or preprint.
  
  https://hal.inria.fr/hal-01296348
• 36M. Nait Abdallah.
  
  On the logic resolution of the wave particle duality paradox in quantum mechanics (Extended abstract), April 2016, working paper or preprint.
  
  https://hal.archives-ouvertes.fr/hal-01303223
• 37J. Papež, Z. Strakoš, M. Vohralík.
  
  Estimating and localizing the algebraic and total numerical errors using flux reconstructions, May 2016, working paper or preprint.
  
  https://hal.inria.fr/hal-01312430
• 38M. Čermák, F. Hecht, Z. Tang, M. Vohralík.
  
  Adaptive inexact iterative algorithms based on polynomial-degree-robust a posteriori estimates for the Stokes problem, January 2017, working paper or preprint.
  
  https://hal.inria.fr/hal-01097662