Publications

Submitted


Accepted

Book chapters

  1. A. Bonito and D. Guignard. Approximating partial differential equations without boundary conditions. In: R. DeVore and A. Kunoth (eds) Multiscale, Nonlinear and Adaptive Approximation, Springer (to appear).
    ArXiv 2406.03634

  2. D. Guignard and O. Mula. Tree-Based Nonlinear Reduced Modeling. In: R. DeVore and A. Kunoth (eds) Multiscale, Nonlinear and Adaptive Approximation, Springer (to appear).
    ArXiv 2404.12262


Journal publications

  1. A. Bonito, D. Guignard, and A. Morvant. Finite Element Methods for the Stretching and Bending of Thin Structures with Folding. To appear in Numerische Mathematik.
    ArXiv 2311.04810

  2. D. Guignard and P. Jantsch. Nonlinear approximation of high-dimensional anisotropic analytic functions. Journal of Approximation Theory, 300:106040, 2024.
    DOI: 10.1016/j.jat.2024.106040 (ArXiv preprint)

  3. A. Bonito, D. Guignard, and W. Lei. Numerical Approximation of Gaussian random fields on Closed Surfaces. Computational Methods in Applied Mathematics, 2024.
    DOI: 10.1515/cmam-2022-0237 (ArXiv preprint)

  4. A. Bonito, D. Guignard, and A. Morvant. Numerical approximations of thin structure deformations. Comptes Rendus. Mécanique, 351 (S1):181-217, 2023.
    DOI: 10.5802/crmeca.201 (ArXiv preprint)

  5. A. Bonito, D. Guignard, R.H. Nochetto, and S. Yang. Numerical analysis of the LDG method for large deformations of prestrained plates. IMA Journal of Numerical Analysis, 43(2):627-662, 2023.
    DOI: 10.1093/imanum/drab103 (ArXiv preprint)

  6. A. Bonito, D. Guignard, R.H. Nochetto, and S. Yang. LDG approximation of large deformations of prestrained plates. Journal of Computational Physics, 448:110719, 2022.
    DOI: 10.1016/j.jcp.2021.110719 (ArXiv preprint)

  7. A. Bonito, V. Girault, D. Guignard, K.R. Rajagopal, and E. Süli. Finite Element Approximation of Steady Flows of Colloidal Solutions. ESAIM: Mathematical Modelling and Numerical Analysis, 55(5):1963-2011, 2021.
    DOI: 10.1051/m2an/2021043 (ArXiv preprint)

  8. A. Bonito, A. Cohen, R. DeVore, D. Guignard, P. Jantsch, and G. Petrova. Nonlinear methods for model reduction. ESAIM: Mathematical Modelling and Numerical Analysis, 55(2):507-531, 2021.
    DOI: 10.1051/m2an/2020057 (ArXiv preprint)

  9. A. Bonito, R. DeVore, D. Guignard, P. Jantsch, and G. Petrova. Polynomial Approximation of Anisotropic Analytic Functions of Several Variables. Constructive Approximation, 53:319-348, 2021.
    DOI: 10.1007/s00365-020-09511-4 (ArXiv preprint)

  10. A. Bonito, D. Guignard, and A.R. Zhang. Reduced basis approximations of the solutions to spectral fractional diffusion problems. Journal of Numerical Mathematics, 28(3):147-160, 2020.
    DOI: 10.1515/jnma-2019-0053 (ArXiv preprint)

  11. D. Guignard. Partial Differential Equations with Random Input Data: A Perturbation Approach. Archives of Computational Methods in Engineering, 26:1313-1377, 2019.
    DOI: 10.1007/s11831-018-9275-2

  12. D. Guignard and F. Nobile. A Posteriori Error Estimation for the Stochastic Collocation Finite Element Method. SIAM Journal on Numerical Analysis, 56(5):3121-3143, 2018.
    DOI: 10.1137/17M1155454

  13. D. Guignard, F. Nobile and M. Picasso. A posteriori error estimation for the steady Navier-Stokes equations in random domains. Computer Methods in Applied Mechanics and Engineering, 313:483-511, 2017.
    DOI: 10.1016/j.cma.2016.10.008

  14. D. Guignard, F. Nobile and M. Picasso. A posteriori error estimation for elliptic partial differential equations with small uncertainties. Numerical Methods for Partial Differential Equations, 32(1):175-212, 2016.
    DOI: 10.1002/num.21991

Conference proceeding

  1. S. Maad, K. Kergrene, J. Vacher, D. Guignard, S. Prudhomme, and A. Rassineux. An Optimal Transport Based hr-Adaptive Mesh Pursuit. 16ème Colloque National en Calcul de Structures, CNRS, CSMA, ENS Paris-Saclay, CentraleSupèlec, Giens, France, May 2024.
    HAL 04610888


Software

  1. A. Bonito and D. Guignard. The deal.ii tutorial step-82: Solving the fourth-order biharmonic equation using a lifting operator approach. 2021.
    DOI: 10.5281/zenodo.5598180/
Contributor: Sparse Grid toolkit, The deal.ii Finite Element Library

Miscellaneous

  1. D. Guignard. A posteriori error estimation for partial differential equations with random input data. PhD Thesis N°7260, Ecole Polytechnique Fédérale de Lausanne, 2016.
    Thesis advisers: Prof. Fabio Nobile and Prof. Marco Picasso.
    DOI: 10.5075/epfl-thesis-7260

  2. D. Guignard. Adaptive data analysis methods for nonlinear and nonstationary data. Master Thesis, California Institute of Technology, 2012.
    Thesis advisers: Prof. Thomas Y. Hou (Caltech) and Prof. Alfio Quarteroni (EPFL).