Daniele A. Di Pietro

Personal information

Full name Daniele Antonio Di Pietro
Roles
  • Full professor of Numerical Analysis
  • Deputy director of Institut Montpelliérain Alexander Grothendieck
  • Head of the ACSIOM research team
  • Affiliation Université de Montpellier
    Curriculum vitæ CV (PDF format)
    Postal address Université de Montpellier
    Institut Montpelliérain Alexander Grothendieck
    Case courrier 051
    place Eugène Bataillon
    34095 Montpellier CEDEX 5, France
    E-mail daniele.di-pietro AT umontpellier.fr

    Research

    Research unit Institut Montpelliérain Alexander Grothendieck (UMR 5149)
    Research interests
  • Advanced numerical methods for PDEs
  • A priori and a posteriori error analysis
  • Fluid and solid mechanics
  • Porous media flows
  • Modern implementation techniques
  • MathSciNet author ID 790640 (requires subscription)
    Scopus author ID 6603444428 (requires subscription)
    ORCID 0000-0003-0959-8830
    Google Scholar Click here
    Highlights
  • New! HArDCore, an HHO-oriented C++ library
  • New! HHO book is out
  • New! Groupe de travail NAGANA
  • POEMS 2019 at CIRM
  • ANR fast4hho
  • ANR HHOMM
  • IHP quarter Numerical Methods for PDEs
  • Publications

    All in one BibTeX file

    Research monographs (2)

    book   1) D. A. Di Pietro and J. Droniou
    The Hybrid High-Order Method for Polytopal Meshes
    Design, Analysis, and Applications
    Number 19 in Modeling, Simulation and Applications
    Springer International Publishing, 2020
    ISBN 978-3-030-37202-6 (Hardcover) 978-3-030-37203-3 (eBook)
    DOI: 10.1007/978-3-030-37203-3
    HAL preprint hal-02151813


    book   2) D. A. Di Pietro and A. Ern
    Mathematical Aspects of Discontinuous Galerkin Methods
    Number 69 in Mathematics & Applications
    Springer-Verlag, Berlin, 2012
    ISBN 978-3-642-22979-4 (Softcover) 978-3-642-22980-0 (eBook)
    DOI: 10.1007/978-3-642-22980-0
    HAL preprint hal-01820185

    Edited monographs (1)

    book   1) D. A. Di Pietro, A. Ern, and L. Formaggia (Eds.)
    Numerical Methods for PDEs: State of the Art Techniques
    Number 15 in SEMA-SIMAI
    Springer International Publishing, 2018
    ISBN 978-3-319-94675-7 (Hardcover) 978-3-319-94676-4 (eBook)
    DOI: 10.1007/978-3-319-94676-4
    HAL preprint hal-01818426

    Papers (61)

    1) D. Castanon Quiroz and D. A. Di Pietro
    A Hybrid High-Order method for the incompressible Navier–Stokes problem robust for large irrotational body forces
    Comput. Math. Appl., 2020, 79(8):2655–2677. DOI: 10.1016/j.camwa.2019.12.005
    HAL preprint hal-02151236

    2) M. Botti, D. A. Di Pietro, O. Le Maître, and P. Sochala
    Numerical approximation of poroelasticity with random coefficients using Polynomial Chaos and Hybrid High-Order methods
    Comput. Meth. Appl. Mech. Engrg., 2020, 361(112736). DOI: 10.1016/j.cma.2019.112736
    HAL preprint hal-02081647, arXiv preprint arXiv:1903.11885

    3) T. Lelièvre, S. Perotto, G. Rozza, D. A. Di Pietro, A. Ern, and L. Formaggia
    Preface: Special Issue on Model Reduction
    J. Sci. Comput., 2019, 81:1–2. DOI: 10.1007/s10915-019-01037-7

    4) M. Botti, D. A. Di Pietro, and P. Sochala
    A Hybrid High-Order discretisation method for nonlinear poroelasticity
    Comput. Meth. Appl. Math., 2020, 20(2):227–249. DOI: 10.1515/cmam-2018-0142
    HAL preprint hal-01785810, arXiv preprint arXiv:1906.00757

    5) M. Botti, D. A. Di Pietro, and A. Guglielmana
    A low-order nonconforming method for linear elasticity on general meshes
    Comput. Meth. Appl. Mech. Engrg., 2019, 354:96–118. DOI: 10.1016/j.cma.2019.05.031
    HAL preprint hal-02009407, arXiv preprint arXiv:1902.02316

    6) L. Botti, D. A. Di Pietro, and J. Droniou
    A Hybrid High-Order method for the incompressible Navier–Stokes equations based on Temam's device
    J. Comput. Phys., 2019, 376:786–816. DOI: 10.1016/j.jcp.2018.10.014
    HAL preprint hal-01867134, arXiv preprint arXiv:1807.07345

    7) F. Chave, D. A. Di Pietro, and L. Formaggia
    A Hybrid High-Order method for passive transport in fractured porous media
    Int. J. Geomath., 2019, 10(12). DOI: 10.1007/s13137-019-0114-x. URL: https://rdcu.be/bjHYw
    HAL preprint hal-01784181

    8) D. A. Di Pietro and J. Droniou
    A third Strang lemma and an Aubin–Nitsche trick for schemes in fully discrete formulation
    Calcolo, 2018, 55(40). DOI: 10.1007/s10092-018-0282-3. URL: https://rdcu.be/5L8F
    HAL preprint hal-01778044, arXiv preprint arXiv:1804.09484

    9) L. Botti and D. A. Di Pietro
    Assessment of Hybrid High-Order methods on curved meshes and comparison with discontinuous Galerkin methods
    J. Comput. Phys., 2018, 370:58–84. DOI: 10.1016/j.jcp.2018.05.017
    HAL preprint hal-01581883

    10) L. Botti, D. A. Di Pietro, and J. Droniou
    A Hybrid High-Order discretisation of the Brinkman problem robust in the Darcy and Stokes limits
    Comput. Meth. Appl. Mech. Engrg., 2018, 341:278–310. DOI: 10.1016/j.cma.2018.07.004
    HAL preprint hal-01746367, arXiv preprint arXiv:1803.10964

    11) J. Aghili and D. A. Di Pietro
    An advection-robust Hybrid High-Order method for the Oseen problem
    J. Sci. Comput., 2018, 77(3):1310–1338. DOI: 10.1007/s10915-018-0681-2
    HAL preprint hal-01658263, arXiv preprint arXiv:1712.02625

    12) D. Boffi and D. A. Di Pietro
    Unified formulation and analysis of mixed and primal discontinuous skeletal methods on polytopal meshes
    ESAIM: Math. Model Numer. Anal., 2018, 52(1):1–28. DOI: 10.1051/m2an/2017036
    HAL preprint hal-01365938, arXiv preprint arXiv:1609.04601

    13) F. Bonaldi, D. A. Di Pietro, G. Geymonat, and F. Krasucki
    A Hybrid High-Order method for Kirchhoff–Love plate bending problems
    ESAIM: Math. Model Numer. Anal., 2018, 52(2):393–421. DOI: 10.1051/m2an/2017065
    HAL preprint hal-01541389, arXiv preprint arXiv:1706.06781

    14) F. Chave, D. A. Di Pietro, and L. Formaggia
    A Hybrid High-Order method for Darcy flows in fractured porous media
    SIAM J. Sci. Comput., 2018, 40(2):A1063–A1094. DOI: 10.1137/17M1119500
    HAL preprint hal-01482925

    15) D. A. Di Pietro, J. Droniou, and G. Manzini
    Discontinuous Skeletal Gradient Discretisation methods on polytopal meshes
    J. Comput. Phys., 2018, 355:397–425. DOI: 10.1016/j.jcp.2017.11.018
    HAL preprint hal-01564598, arXiv preprint arXiv:1706.09683

    16) D. A. Di Pietro and F. Marche
    Weighted Interior Penalty discretization of fully nonlinear and weakly dispersive free surface shallow water flows
    J. Comput. Phys., 2018, 355:285–309. DOI: 10.1016/j.jcp.2017.11.009
    HAL preprint hal-01566446

    17) D. A. Di Pietro and S. Krell
    A Hybrid High-Order method for the steady incompressible Navier–Stokes problem
    J. Sci. Comput., 2018, 74(3):1677–1705. DOI: 10.1007/s10915-017-0512-x
    HAL preprint hal-01349519, arXiv preprint arXiv:1607.08159

    18) M. Cicuttin, D. A. Di Pietro, and A. Ern
    Implementation of Discontinuous Skeletal methods on arbitrary-dimensional, polytopal meshes using generic programming
    J. Comput. Appl. Math., 2018, 344:852–874. DOI: 10.1016/j.cam.2017.09.017
    HAL preprint hal-01429292

    19) J. Aghili, D. A. Di Pietro, and B. Ruffini
    An $hp$-Hybrid High-Order method for variable diffusion on general meshes
    Comput. Meth. Appl. Math., 2017, 17(3):359–376. DOI: 10.1515/cmam-2017-0009
    HAL preprint hal-01290251

    20) M. Botti, D. A. Di Pietro, and P. Sochala
    A Hybrid High-Order method for nonlinear elasticity
    SIAM J. Numer. Anal., 2017, 55(6):2687–2717. DOI: 10.1137/16M1105943
    HAL preprint hal-01539510, arXiv preprint arXiv:1707.02154

    21) D. A. Di Pietro and J. Droniou
    $W^{s,p}$-approximation properties of elliptic projectors on polynomial spaces, with application to the error analysis of a Hybrid High-Order discretisation of Leray–Lions problems
    Math. Models Methods Appl. Sci., 2017, 27(5):879–908. DOI: 10.1142/S0218202517500191
    HAL preprint hal-01326818, arXiv preprint arXiv:1606.02832

    22) D. A. Di Pietro and J. Droniou
    A Hybrid High-Order method for Leray–Lions elliptic equations on general meshes
    Math. Comp., 2017, 86(307):2159–2191. DOI: 10.1090/mcom/3180
    HAL preprint hal-01183484, arXiv preprint arXiv:1508.01918

    23) D. A. Di Pietro and A. Ern
    Arbitrary-order mixed methods for heterogeneous anisotropic diffusion on general meshes
    IMA J. Numer. Anal., 2017, 37(1):40–63. DOI: 10.1093/imanum/drw003
    HAL preprint hal-00918482

    24) D. A. Di Pietro, B. Kapidani, R. Specogna, and F. Trevisan
    An arbitrary-order discontinuous skeletal method for solving electrostatics on general polyhedral meshes
    IEEE Transactions on Magnetics, 2017, 53(6):1–4. DOI: 10.1109/TMAG.2017.2666546
    HAL preprint hal-01399505

    25) R. Riedlbeck, D. A. Di Pietro, A. Ern, S. Granet, and K. Kazymyrenko
    Stress and flux reconstruction in Biot's poro-elasticity problem with application to a posteriori error analysis
    Comput. Math. Appl., 2017, 73(7):1593–1610. DOI: 10.1016/j.camwa.2017.02.005
    HAL preprint hal-01366646

    26) D. Boffi, M. Botti, and D. A. Di Pietro
    A nonconforming high-order method for the Biot problem on general meshes
    SIAM J. Sci. Comput., 2016, 38(3):A1508–A1537. DOI: 10.1137/15M1025505
    HAL preprint hal-01162976, arXiv preprint arXiv:1506.03722

    27) F. Chave, D. A. Di Pietro, F. Marche, and F. Pigeonneau
    A Hybrid High-Order method for the Cahn–Hilliard problem in mixed form
    SIAM J. Numer. Anal., 2016, 54(3):1873–1898. DOI: 10.1137/15M1041055
    HAL preprint hal-01203733, arXiv preprint arXiv:1509.07384

    28) B. Cockburn, D. A. Di Pietro, and A. Ern
    Bridging the Hybrid High-Order and Hybridizable Discontinuous Galerkin methods
    ESAIM: Math. Model Numer. Anal., 2016, 50(3):635–650. DOI: 10.1051/m2an/2015051
    HAL preprint hal-01115318

    29) D. A. Di Pietro, A. Ern, A. Linke, and F. Schieweck
    A discontinuous skeletal method for the viscosity-dependent Stokes problem
    Comput. Meth. Appl. Mech. Engrg., 2016, 306:175–195. DOI: 10.1016/j.cma.2016.03.033
    HAL preprint hal-01244387

    30) D. A. Di Pietro and R. Specogna
    An a posteriori-driven adaptive Mixed High-Order method with application to electrostatics
    J. Comput. Phys., 2016, 326(1):35–55. DOI: 10.1016/j.jcp.2016.08.041
    HAL preprint hal-01310313

    31) J. Aghili, S. Boyaval, and D. A. Di Pietro
    Hybridization of mixed high-order methods on general meshes and application to the Stokes equations
    Comput. Meth. Appl. Math., 2015, 15(2):111–134. DOI: 10.1515/cmam-2015-0004
    HAL preprint hal-01009723

    32) J. Bonelle, D. A. Di Pietro, and A. Ern
    Low-order reconstruction operators on polyhedral meshes: Application to Compatible Discrete Operator schemes
    Computer Aided Geometric Design, 2015, 35–36:27–41. DOI: 10.1016/j.cagd.2015.03.015
    HAL preprint hal-01097311

    33) D. A. Di Pietro, J. Droniou, and A. Ern
    A discontinuous-skeletal method for advection-diffusion-reaction on general meshes
    SIAM J. Numer. Anal., 2015, 53(5):2135–2157. DOI: 10.1137/140993971
    HAL preprint hal-01079342, arXiv preprint arXiv:1411.0098

    34) D. A. Di Pietro and A. Ern
    Equilibrated tractions for the Hybrid High-Order method
    C. R. Acad. Sci. Paris, Ser. I, 2015, 353:279–282. DOI: 10.1016/j.crma.2014.12.009
    HAL preprint hal-01079026, arXiv preprint arXiv:1411.0094

    35) D. A. Di Pietro and A. Ern
    Hybrid high-order methods for variable-diffusion problems on general meshes
    C. R. Acad. Sci. Paris, Ser. I, 2015, 353:31–34. DOI: 10.1016/j.crma.2014.10.013
    HAL preprint hal-01023302

    36) D. A. Di Pietro and A. Ern
    A hybrid high-order locking-free method for linear elasticity on general meshes
    Comput. Meth. Appl. Mech. Engrg., 2015, 283:1–21. DOI: 10.1016/j.cma.2014.09.009
    HAL preprint hal-00979435

    37) D. A. Di Pietro and S. Lemaire
    An extension of the Crouzeix–Raviart space to general meshes with application to quasi-incompressible linear elasticity and Stokes flow
    Math. Comp., 2015, 84(291):1–31. DOI: 10.1090/S0025-5718-2014-02861-5
    HAL preprint hal-00753660

    38) D. A. Di Pietro, M. Vohralík, and S. Yousef
    Adaptive regularization, linearization, discretization, and a posteriori error control for the two-phase Stefan problem
    Math. Comp., 2015, 84(291):153–186. DOI: 10.1090/S0025-5718-2014-02854-8
    HAL preprint hal-00690862

    39) D. A. Di Pietro, A. Ern, and S. Lemaire
    An arbitrary-order and compact-stencil discretization of diffusion on general meshes based on local reconstruction operators
    Comput. Meth. Appl. Math., 2014, 14(4):461–472. Open access (editor's choice). DOI: 10.1515/cmam-2014-0018
    HAL preprint hal-00978198

    40) D. A. Di Pietro, E. Flauraud, M. Vohralík, and S. Yousef
    A posteriori error estimates, stopping criteria, and adaptivity for multiphase compositional Darcy flows in porous media
    J. Comput. Phys., 2014, 274:163–187. DOI: 10.1016/j.jcp.2014.06.061
    HAL preprint hal-00839487

    41) D. A. Di Pietro, M. Vohralík, and S. Yousef
    An a posteriori-based, fully adaptive algorithm for thermal multiphase compositional flows in porous media with adaptive mesh refinement
    Comput. Math. Appl., 2014, 68(12):2331–2347. DOI: 10.1016/j.camwa.2014.08.008
    HAL preprint hal-00856437

    42) D. A. Di Pietro and M. Vohralík
    A review of recent advances in discretization methods, a posteriori error analysis, and adaptive algorithms for numerical modeling in geosciences
    Oil & Gas Science and Technology, 2014, 69(4):701–730. DOI: 10.2516/ogst/2013158
    HAL preprint hal-00783068

    43) D. A. Di Pietro, J.-M. Gratien, and C. Prud'homme
    A domain-specific embedded language in C++ for lowest-order discretizations of diffusive problems on general meshes
    BIT Numerical Mathematics, 2013, 53(1):111–152. DOI: 10.1007/s10543-012-0403-3
    HAL preprint hal-00654406

    44) D. A. Di Pietro and S. Nicaise
    A locking-free discontinuous Galerkin method for linear elasticity in locally nearly incompressible heterogeneous media
    App. Num. Math., 2013, 63:105–116. DOI: 10.1016/j.apnum.2012.09.009
    HAL preprint hal-00685020

    45) D. A. Di Pietro
    On the conservativity of cell centered Galerkin methods
    C. R. Acad. Sci. Paris, Ser. I, 2013, 351(3–4):155–159. DOI: 10.1016/j.crma.2013.03.001
    HAL preprint hal-00781510

    46) F. Bassi, L. Botti, A. Colombo, D. A. Di Pietro, and P. Tesini
    On the flexibility of agglomeration based physical space discontinuous Galerkin discretizations
    J. Comput. Phys., 2012, 231(1):45–65. DOI: 10.1016/j.jcp.2011.08.018
    HAL preprint hal-00562219

    47) D. A. Di Pietro and A. Ern
    Analysis of a discontinuous Galerkin method for heterogeneous diffusion problems with low-regularity solutions
    Numer. Meth. for PDEs, 2012, 28(4):1161–1177. DOI: 10.1002/num.20675
    HAL preprint hal-00514387

    48) D. A. Di Pietro
    Cell centered Galerkin methods for diffusive problems
    ESAIM: Math. Model Numer. Anal., 2012, 46(1):111–144. DOI: 10.1051/m2an/2011016
    HAL preprint hal-00511125

    49) L. Botti and D. A. Di Pietro
    A pressure-correction scheme for convection-dominated incompressible flows with discontinuous velocity and continuous pressure
    J. Comput. Phys., 2011, 230(3):572–585. DOI: 10.1016/j.jcp.2010.10.004
    HAL preprint hal-00458293

    50) D. A. Di Pietro
    A compact cell-centered Galerkin method with subgrid stabilization
    C. R. Acad. Sci. Paris, Ser. I, 2011, 349(1–2):93–98. DOI: 10.1016/j.crma.2010.11.017
    HAL preprint hal-00476222

    51) L. Agélas, D. A. Di Pietro, and J. Droniou
    The G method for heterogeneous anisotropic diffusion on general meshes
    ESAIM: Math. Model Numer. Anal., 2010, 44(4):597–625. DOI: 10.1051/m2an/2010021
    HAL preprint hal-00342739

    52) L. Agélas, D. A. Di Pietro, R. Eymard, and R. Masson
    An abstract analysis framework for nonconforming approximations of diffusion problems on general meshes
    IJFV International Journal on Finite Volumes, 2010, 7(1):1–29
    HAL preprint hal-00318390

    53) D. A. Di Pietro and A. Ern
    Discrete functional analysis tools for discontinuous Galerkin methods with application to the incompressible Navier–Stokes equations
    Math. Comp., 2010, 79:1303–1330. DOI: 10.1090/S0025-5718-10-02333-1
    HAL preprint hal-00278925

    54) D. A. Di Pietro
    Cell centered Galerkin methods
    C. R. Acad. Sci. Paris, Ser. I, 2010, 348(1–2):31–34. DOI: 10.1016/j.crma.2009.11.012
    HAL preprint hal-00398782

    55) D. A. Di Pietro and A. Veneziani
    Expression template implementation of continuous and discontinuous Galerkin methods
    Comp. Vis. in Sci., 2009, 12:421–436. DOI: 10.1007/s00791-008-0117-x
    HAL preprint hal-01818198

    56) D. A. Di Pietro, A. Ern, and J.-L. Guermond
    Discontinuous Galerkin methods for anisotropic semi-definite diffusion with advection
    SIAM J. Numer. Anal., 2008, 46(2):805–831. DOI: 10.1137/060676106
    HAL preprint hal-01818201

    57) F. Bassi, A. Crivellini, D. A. Di Pietro, and S. Rebay
    An implicit high-order discontinuous Galerkin method for steady and unsteady incompressible flows
    Comp. & Fl., 2007, 36(10):1529–1546. DOI: 10.1016/j.compfluid.2007.03.012
    HAL preprint hal-01818204

    58) D. A. Di Pietro
    Analysis of a discontinuous Galerkin approximation of the Stokes problem based on an artificial compressibility flux
    Int. J. Num. Meth. Fluids, 2007, 55(8):793–813. DOI: 10.1002/fld.1495
    HAL preprint hal-01818207

    59) F. Bassi, A. Crivellini, D. A. Di Pietro, and S. Rebay
    An artificial compressibility flux for the discontinuous Galerkin solution of the incompressible Navier-Stokes equations
    J. Comput. Phys., 2006, 218(2):794–815. DOI: 10.1016/j.jcp.2006.03.006
    HAL preprint hal-01818209

    60) D. A. Di Pietro, S. Lo Forte, and N. Parolini
    Mass preserving finite element implementations of the level set method
    App. Num. Math., 2006, 56:1179–1195. DOI: 10.1016/j.apnum.2006.03.003
    HAL preprint hal-01818211

    61) G. E. Cossali, D. A. Di Pietro, and M. Marengo
    Comparison of four analytical and numerical models for a microchannel heat sink
    Int. J. Heat and Tech., 2003, 21(2):31–42
    HAL preprint hal-01820286

    Book chapters (4)

    1) L. Botti, M. Botti, and D. A. Di Pietro
    A Hybrid High-Order method for multiple-network poroelasticity
    in Polyhedral Methods in Geosciences, D. A. Di Pietro, L. Formaggia, R. Masson eds., Springer, 2020. Accepted for publication
    HAL preprint hal-02461755

    2) D. A. Di Pietro, A. Ern, and L. Formaggia
    An introduction to recent developments in numerical methods for partial differential equations
    in Numerical Methods for PDEs: State of the Art Techniques, D. A. Di Pietro, A. Ern, L. Formaggia eds., Springer, 2018
    DOI: 10.1007/978-3-319-94676-4_1 , ISBN: 978-3-319-94675-7 (Print) 978-3-319-94676-4 (eBook)
    HAL preprint hal-01490524, arXiv preprint arXiv:1703.05136

    3) D. A. Di Pietro and R. Tittarelli
    An introduction to Hybrid High-Order methods
    in Numerical Methods for PDEs: State of the Art Techniques, D. A. Di Pietro, A. Ern, L. Formaggia eds., Springer, 2018
    DOI: 10.1007/978-3-319-94676-4_4 , ISBN: 978-3-319-94675-7 (Print) 978-3-319-94676-4 (eBook)
    HAL preprint hal-01490524, arXiv preprint arXiv:1703.05136

    4) D. A. Di Pietro, A. Ern, 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, Barrenechea, G. and Brezzi, F. and Cangiani, A. and Georgoulis, M. eds., Springer, 2016. No 114 in Lecture Notes in Computational Science and Engineering
    DOI: 10.1007/978-3-319-41640-3 , ISBN: 978-3-319-41638-0 (Print) 978-3-319-41640-3 (eBook)
    HAL preprint hal-01163569

    Preprints (5)

    1) D. A. Di Pietro and J. Droniou
    An arbitrary-order method for magnetostatics on polyhedral meshes based on a discrete de Rham sequence
    HAL preprint hal-02573274, arXiv preprint arXiv:2005.06890, May 2020

    2) M. Botti, D. Castanon Quiroz, D. A. Di Pietro, and A. Harnist
    A Hybrid High-Order method for creeping flows of non-Newtonian fluids
    HAL preprint hal-02519233, arXiv preprint arXiv:2003.13467, March 2020

    3) P. Matalon, D. A. Di Pietro, P. Mycek, U. Rüde, and D. Ruiz
    An $h$-multigrid method for Hybrid High-Order discretizations
    HAL preprint hal-02434411, January 2020

    4) L. Botti, M. Botti, and D. A. Di Pietro
    An abstract analysis framework for monolithic discretisations of poroelasticity with application to Hybrid High-Order methods
    HAL preprint hal-02398946, arXiv preprint arXiv:1912.03665, December 2019

    5) D. A. Di Pietro, J. Droniou, and F. Rapetti
    Fully discrete polynomial de Rham sequences of arbitrary degree on polygons and polyhedra
    HAL preprint hal-02356810, arXiv preprint arXiv:1911.03616, November 2019

    Proceedings (19)

    1) F. Chave, D. A. Di Pietro, and S. Lemaire
    A three-dimensional Hybrid High-Order method for magnetostatics
    Finite Volumes for Complex Applications IX, 2020. Accepted for publication
    Preprint hal-02407175

    2) M. Botti, D. A. Di Pietro, and P. Sochala
    A nonconforming high-order method for nonlinear poroelasticity
    Finite Volumes for Complex Applications VIII – Hyperbolic, Elliptic and Parabolic Problems, 2017 p. 537–546
    DOI: 10.1007/978-3-319-57397-7
    Preprint hal-01439165

    3) F. Chave, D. A. Di Pietro, and F. Marche
    A Hybrid High-Order method for the convective Cahn–Hilliard problem in mixed form
    Finite Volumes for Complex Applications VIII – Hyperbolic, Elliptic and Parabolic Problems, 2017 p. 517–526
    DOI: 10.1007/978-3-319-57397-7
    Preprint hal-01477247

    4) D. A. Di Pietro and S. Krell
    Benchmark session: The 2D Hybrid High-Order method
    Finite Volumes for Complex Applications VIII – Methods and Theoretical Aspects, 2017 p. 91–106
    DOI: 10.1007/978-3-319-57397-7
    Preprint hal-01818217

    5) R. Riedlbeck, D. A. Di Pietro, and A. Ern
    Equilibrated stress reconstruction for linear elasticity problems with application to a posteriori error analysis
    Finite Volumes for Complex Applications VIII – Methods and Theoretical Aspects, 2017 p. 293–302
    Preprint hal-01433841

    6) D. A. Di Pietro, R. Eymard, S. Lemaire, and R. Masson
    Hybrid finite volume discretization of linear elasticity models on general meshes
    Finite Volumes for Complex Applications VI, 2011 p. 331–339
    DOI: 10.1007/978-3-642-20671-9_35
    Preprint hal-00795201

    7) D. A. Di Pietro and J.-M. Gratien
    Lowest order methods for diffusive problems on general meshes: A unified approach to definition and implementation
    Finite Volumes for Complex Applications VI, 2011 p. 3–19. Invited paper
    DOI: 10.1007/978-3-642-20671-9_84
    Preprint hal-00562500

    8) D. A. Di Pietro, M. Vohralík, and C. Widmer
    An a posteriori error estimator for a finite volume discretization of two-phase flow
    Finite Volumes for Complex Applications VI, 2011 p. 341–349
    DOI: 10.1007/978-3-642-20671-9_36

    9) L. Agélas, D. A. Di Pietro, and I. Kapyrin
    A comparison of last generation cell centered finite volume methods on challenging three dimensional problems
    Proceedings of the 3rd International Conference on Approximation Methods and numerical Modeling in Environment and Natural Resources, 2009

    10) L. Agélas, D. A. Di Pietro, I. Kapyrin, and R. Masson
    Generalized L-scheme for the discretization of diffusion fluxes on general meshes
    Proceedings of the 11th European Conference on the Mathematics of Oil Recovery, 2008

    11) L. Agélas, D. A. Di Pietro, R. Eymard, and R. Masson
    A general framework for non-conforming approximations of the single phase Darcy equation
    Proceedings of the 11th European Conference on the Mathematics of Oil Recovery, 2008

    12) L. Agélas, D. A. Di Pietro, I. Kapyrin, and R. Masson
    The MPFA G scheme for heterogeneous anisotropic diffusion problems on general meshes
    Proceedings of the 11th European Conference on the Mathematics of Oil Recovery, 2008

    13) L. Agélas, D. A. Di Pietro, and R. Masson
    A symmetric and coercive finite volume scheme for multiphase porous media flow with applications in the oil industry
    Finite Volumes for Complex Applications V, 2008 p. 35–52. Invited paper
    Preprint hal-01818220
    ISBN: 978-1-84821-035-6

    14) L. Agélas and D. A. Di Pietro
    A symmetric finite volume scheme for anisotropic heterogeneous second-order elliptic problems
    Finite Volumes for Complex Applications V, 2008 p. 705–716
    ISBN: 978-1-84821-035-6

    15) D. A. Di Pietro and A. Ern
    A discontinuous Galerkin flux for anisotropic heterogeneous second-order elliptic problems
    Finite Volumes for Complex Applications V, 2008 p. 777–793
    Preprint hal-01818221
    ISBN: 978-1-84821-035-6

    16) S. Mundal, D. A. Di Pietro, and I. Aavatsmark
    Compact-stencil MPFA method for heterogeneous highly-anisotropic second order elliptic problems
    Finite Volumes for Complex Applications V, 2008 p. 905–918
    Preprint hal-01818222
    ISBN: 978-1-84821-035-6

    17) F. Bassi, A. Crivellini, D. A. Di Pietro, and S. Rebay
    A high-order discontinuous Galerkin solver for 3D aerodynamic turbulent flows
    ECCOMAS CFD 2006 Proceedings (Egmond an Zee, Netherlands), 2006

    18) G. E. Cossali, D. A. Di Pietro, and M. Marengo
    Analytical and numerical modeling of microchannel heat sinks
    Proceedings of the First International Conference on Microchannels and Minichannels (Rochester, New York), 2003

    19) G. E. Cossali, D. A. Di Pietro, and M. Marengo
    Design of a microchannel cooling system for BTeV particle detector
    Proceedings of the 8th International Workshop on Thermal Investigations of ICs and Systems (Madrid, Spain), 2002

    Theses (2)

    1) D. A. Di Pietro
    Méthodes non conformes pour des équations aux dérivées partielles avec diffusion
    HDR thesis, Université de Paris-Est, 6 December 2010
    Manuscript tel-00550230

    2) D. A. Di Pietro
    Discontinuous Galerkin methods for the incompressible Navier–Stokes equations
    PhD thesis, Università di Bergamo, 3 March 2006

    Some presentations

    1) Hybrid High-Order methods for poroelasticity [slides]
    IFP Energies Nouvelles, 4 December 2019

    2) Hybrid High-Order methods for poroelasticity [slides]
    Université de Franche-Comté, 2 October 2019

    3) Recent advances on Hybrid High-Order methods for problems in incompressible fluid mechanics [slides]
    ICIAM 2019, 16 July 2019

    4) Hybrid High-Order methods for diffusion problems on polytopes and curved elements [slides]
    MAFELAP 2019, 19 June 2019

    5) An introduction to Hybrid High-Order methods with applications to incompressible fluid mechanics [slides]
    Université de Nice Sophia Antipolis, 16 May 2019

    6) Hybrid High-Order methods for elasticity [slides]
    POEMS 2019, 3 May 2019

    7) An introduction to Hybrid High-Order methods with applications to incompressible fluid mechanics [slides]
    SISSA, 7 March 2019

    8) A Hybrid High-Order method for incompressible Navier–Stokes equations based on Temam's device [slides]
    Università di Udine, 30 October 2018

    9) A Hybrid High-Order method for incompressible Navier–Stokes equations based on Temam's device [slides]
    EDF, 28 June 2018

    10) An introduction to Hybrid High-Order methods with application to the incompressible Navier–Stokes equations [slides]
    Montpellier, 19 June 2018

    11) A non-standard application of the Raviart–Thomas–Nédélec element: A HHO method for the Brinkman problem robust in the Darcy and Stokes limits [slides]
    CANUM 2018, 29 May 2018. See also here for a stable high-order gradient reconstruction on general meshes based on the Raviart–Thomas–Nédélec element

    12) An introduction to the convergence analysis of discretisation methods for PDEs with application to Hybrid High-Order methods [slides]
    Università di Bergamo, 10-11 May 2018. See also here for the discrete analysis framework and here for an introduction to HHO methods

    13) An introduction to Hybrid High-Order methods [slides]
    CERFACS, 9 February 2018

    14) An introduction to Hybrid High-Order methods - Nonlinear elasticity and poroelasticity [slides]
    Università di Bergamo, 19 December 2017

    15) An introduction to Hybrid High-Order methods - Nonlinear elasticity and poroelasticity [slides]
    Journées Multiphasiques et Incertitudes, Nantes, 14 November 2017

    16) Recent advances on Hybrid High-Order methods for linear and nonlinear problems [slides]
    POEMS 2017, Milan, 5 July 2017

    17) Recent advances on Hybrid High-Order methods for nonlinear problems [slides]
    MOX, Politecnico di Milano, 20 December 2016

    18) Hybrid High-Order methods [slides]
    Institut Henri Poincaré thematic quarter Numerical Methods for PDEs, 13-14 September 2016

    19) A Hybrid High-Order method for Leray–Lions equations [slides]
    MAFELAP 2016, 16 June 2016

    20) Bridging the Hybrid High-Order and Hybridizable Discontinuous Galerkin Methods [slides]
    MAFELAP 2016, 15 June 2016

    21) Hybrid High-Order methods on general meshes [slides]
    Universität Zürich, 20 April 2016

    22) An a posteriori-based fully adaptive algorithm for the two-phase Stefan problem [slides]
    Università di Pavia, 23 February 2016

    23) A Hybrid High-Order method for locally degenerate advection-diffusion-reaction [slides]
    X-DMS 2015, Ferrara, 10 September 2015

    24) An introduction to Hybrid High-Order methods [slides]
    CEA-EDF-INRIA School New trends in Compatible Discretizations, INRIA Roquencourt, 29 June 2015

    25) Hybrid High-Order (HHO) methods on general meshes [slides]
    Journée Méthode de Galerkine discontinue et ses applications, CNAM, Paris, 19 June 2015

    26) Hybrid and mixed high-order methods [slides]
    Università Milano Bicocca, 12 February 2015

    27) Hybrid High-Order methods for degenerate advection-diffusion-reaction [slides]
    Séminaire Modélisation mathématique et calcul scientifique ICJ, Lyon, 20 January 2015

    28) Hybrid high-order methods for quasi-incompressible linear elasticity on general meshes [slides]
    WCCM XI, Barcelona, 24 July 2014

    29) A family of arbitrary-order mixed methods for anisotropic heterogeneous diffusion [slides]
    GT Calcul Scientifique, UM2, 14 February 2014

    30) A posteriori error estimates, stopping criteria, and adaptivity for multiphase compositional Darcy flows in porous media [slides]
    LATP, Université Aix Marseille, 1 October 2013

    31) Discontinuous Galerkin methods and applications [slides]
    École de Mécanique des Fluides Numériques, Porquerolles, 2–8 June 2013

    32) An extension of the Crouzeix–Raviart and Raviart–Thomas spaces to general meshes [slides]
    MOX, Politecnico di Milano, 26 February 2013

    33) A hybrid finite volume generalization of the Crouzeix-Raviart element [slides]
    GDR MoMaS workshop, Marseille, 15 October 2012

    34) Locking-free numerical approximations of the elasticity operator [slides]
    Workshop on complex grids and fluid flows, 2 April 2012

    35) Cell centered Galerkin methods for diffusive problems on general meshes [slides]
    Università di Bergamo, 21 December 2011

    36) Recent advances on nonconforming methods for diffusive problems on general meshes [slides]
    University of Montpellier 2, 8 November 2011

    37) Lowest order methods for diffusive problems on general meshes [slides]
    Finite Volumes for Complex Applications VI, Prague, 8 June 2011

    38) Nonconforming methods for PDEs with diffusion [slides]
    University of Sussex, Brighton, 6 May 2011

    Press

    MaddMaths interview (in Italian)

    Teaching

    Teaching component Faculté des Sciences
    Teaching department Département de Mathématiques
    Highlights Master Modélisation et Analyse Numérique

    Introduction to HHO methods [here]
    Notes du cours d'Analyse Numérique Matricielle (version provisoire permanente) [here]

    Updated 1/6/2020