Submitted

1. D. Guignard and O. Mula. Tree-Based Nonlinear Reduced Modeling.
   ArXiv 2404.12262


2. A. Bonito, D. Guignard, and A. Morvant. Finite Element Methods for the Stretching and Bending of Thin Structures with Folding.
   ArXiv 2311.04810

Accepted journal publications

1. D. Guignard and P. Jantsch. Nonlinear approximation of high-dimensional anisotropic analytic functions. To appear in Journal of Approximation Theory.
   ArXiv 2210.07067


2. A. Bonito, D. Guignard, and W. Lei. Numerical Approximation of Gaussian random fields on Closed Surfaces. To appear in Computational Methods in Applied Mathematics.
   ArXiv 2211.13739


3. A. Bonito, D. Guignard, and A. Morvant. Numerical approximations of thin structure deformations. Comptes Rendus Mécanique, Online first:1-37, 2023.
   DOI: 10.5802/crmeca.201


4. 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


5. 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


6. 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


7. 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


8. 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


9. 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


10. 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


11. 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


12. 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


13. 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

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).