Publications

Journal articles

• A. Abdulle (†) and SL. An optimization-based method for sign-changing elliptic PDEs. To appear in ESAIM Math. Model. Numer. Anal., 2024. DOI: 10.1051/m2an/2024013.

• SL and S. Pitassi. Discrete Weber inequalities and related Maxwell compactness for hybrid spaces over polyhedral partitions of domains with general topology. To appear in Found. Comput. Math., 2024. DOI: 10.1007/s10208-024-09648-9.

• SL and J. Moatti. Structure preservation in high-order hybrid discretisations of potential-driven advection-diffusion: linear and nonlinear approaches. Math. Eng., Special Issue: Advancements in Polytopal Element Methods, 6(1):100-136, 2024. DOI: 10.3934/mine.2024005.

• C. Chainais-Hillairet, M. Herda, SL, and J. Moatti. Long-time behaviour of hybrid finite volume schemes for advection-diffusion equations: linear and nonlinear approaches. Numer. Math., 151(4):963-1016, 2022. DOI: 10.1007/s00211-022-01289-w.

• T. Chaumont-Frelet, A. Ern, SL, and F. Valentin. Bridging the Multiscale Hybrid-Mixed and Multiscale Hybrid High-Order methods. ESAIM Math. Model. Numer. Anal., 56(1):261-285, 2022. DOI: 10.1051/m2an/2021082.

• F. Chave, D. A. Di Pietro, and SL. A discrete Weber inequality on three-dimensional hybrid spaces with application to the HHO approximation of magnetostatics. Math. Models Methods Appl. Sci., 32(1):175-207, 2022. DOI: 10.1142/S0218202522500051.

• SL. Bridging the Hybrid High-Order and Virtual Element methods. IMA J. Numer. Anal., 41(1):549-593, 2021. DOI: 10.1093/imanum/drz056.

• M. Cicuttin, A. Ern, and SL. A Hybrid High-Order method for highly oscillatory elliptic problems. Comput. Methods Appl. Math., 19(4):723-748, 2019. DOI: 10.1515/cmam-2018-0013.

• C. Le Bris, F. Legoll, and SL. On the best constant matrix approximating an oscillatory matrix-valued coefficient in divergence-form operators. ESAIM Control Optim. Calc. Var., 24(4):1345-1380, 2018. DOI: 10.1051/cocv/2017061.

• A. Abdulle, M. E. Huber, and SL. An optimization-based numerical method for diffusion problems with sign-changing coefficients. Comptes Rendus. Mathématique, 355(4):472-478, 2017. DOI: 10.1016/j.crma.2017.02.010.

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

• D. A. Di Pietro, A. Ern, and SL. An arbitrary-order and compact-stencil discretization of diffusion on general meshes based on local reconstruction operators. Comput. Methods Appl. Math., 14(4):461-472, 2014. DOI: 10.1515/cmam-2014-0018.

Book chapter

• D. A. Di Pietro, A. Ern, and SL. 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, G. R. Barrenechea, F. Brezzi, A. Cangiani, E. H. Georgoulis (eds.), Lecture Notes in Computational Science and Engineering, 114:205-236, Springer, Cham, 2016. DOI: 10.1007/978-3-319-41640-3_7.

Conference proceedings

• F. Chave, D. A. Di Pietro, and SL. A three-dimensional Hybrid High-Order method for magnetostatics. In Finite Volumes for Complex Applications IX - Methods, Theoretical Aspects, Examples, R. Klöfkorn, E. Keilegavlen, F. A. Radu, J. Fuhrmann (eds.), Springer Proceedings in Mathematics & Statistics, 323:255-263, Springer, Cham, 2020. DOI: 10.1007/978-3-030-43651-3_22.

• M. Cicuttin, A. Ern, and SL. On the implementation of a multiscale Hybrid High-Order method. In Numerical Mathematics and Advanced Applications - ENUMATH 2017, F. A. Radu, K. Kumar, I. Berre, J. M. Nordbotten, I. S. Pop (eds.), Lecture Notes in Computational Science and Engineering, 126:509-517, Springer, Cham, 2019. DOI: 10.1007/978-3-319-96415-7_46.

• D. A. Di Pietro, R. Eymard, SL, and R. Masson. Hybrid finite volume discretization of linear elasticity models on general meshes. In Finite Volumes for Complex Applications VI - Problems & Perspectives, J. Fořt, J. Fürst, J. Halama, R. Herbin, F. Hubert (eds.), Springer Proceedings in Mathematics, 4:331-339, Springer, Berlin-Heidelberg, 2011. DOI: 10.1007/978-3-642-20671-9_35.

Software

• L. Beaude and SL. ParaSkel++: a C++ platform for the high-performance, arbitrary-order, 2/3D numerical approximation of PDEs on general polytopal meshes using skeletal Galerkin methods. Version v1, under GNU LGPL v3, Aug. 2021.

Dissertations

• PhD thesis (2013): Nonconforming discretizations of a poromechanical model on general meshes - PDF (introduction/perspectives in French, body in English), Slides of the defense (in English) [Finalist of the 2014 AMIES thesis prize]

• Master thesis (2010): Relaxation schemes for the Baer-Nunziato compressible two-phase flow model in ALE formulation - PDF (in French), Slides of the defense (in French)

Miscellaneous

• Some insight on Hybrid High-Order methods - PDF (in French)