About me

I am a Postdoctoral Research Associate in the Department of Mathematics at University of Arizona, Tucson, AZ. Previously, I was a Visiting Assistant Professor in the Department of Engineering Sciences and Applied Mathematics (ESAM) at Northwestern University, Evanston, IL (2022–2024). My research focuses on the numerical analysis of partial differential equations, with an emphasis on finite element methods, spectral methods, and Trefftz/quasi-Trefftz approaches. I work on a posteriori error analysis, contact and interface problems in solid mechanics, and the development of constitutive models for engineering applications such as dam modeling.

You can reach me at ifontana@arizona.edu.

Education

Ph.D. in Mathematics and Modelisation, University of Montpellier and EDF Lab Paris-Saclay (CIFRE industrial agreement), France, 2022

M.S. in Applied Mathematics, University of Udine, Italy, 2018

B.S. in Mathematics, University of Udine, Italy, 2016

Research

Research interests:

Numerical methods for PDEs (FEM, Trefftz and quasi-Trefftz methods, tau spectral methods)
A posteriori error analysis and adaptive algorithms
Contact problems
Solid mechanics and electromagnetims
Constitutive relations for joints and materials

Publications

Articles, Conference Papers and Preprints

  • I. Fontana, L.-M. Imbert-Gérard, Quasi-Trefftz spaces for the first-order time-harmonic Maxwell's equations, 2026.
    - [arXiv]

  • I. Fontana, G. Bacquaert, D. A. Di Pietro, K. Kazymyrenko, Hyperelastic nature of the Hoek-Brown criterion, European Journal of Mechanics - A/Solids, 2026, 115:105782.
    - DOI: 10.1016/j.euromechsol.2025.105782
    - [arXiv], [Hal]

  • I. Fontana, L.-M. Imbert-Gérard, Generalized Plane Wave quasi-Trefftz spaces for wave propagation in inhomogeneous media, Proceedings of the 11th Convention of the European Acoustics Association Forum Acusticum / EuroNoise 2025, 2025.
    - DOI: 10.61782/fa.2025.0967
    - [arXiv]

  • I. Fontana, D. A. Di Pietro, An a posteriori error analysis based on equilibrated stresses for finite element approximations of frictional contact. Computer Methods in Applied Mechanics and Engineering, 2024, 425:116950.
    - DOI: 10.1016/j.cma.2024.116950
    - Preprint: arXiv, Hal

  • D. A. Di Pietro, I. Fontana, K. Kazymyrenko, A posteriori error estimates via equilibrated stress reconstructions for contact problems approximated by Nitsche's method. Computers & Mathematics with Applications, 2022, 111:61-80.
    - DOI: 10.1016/j.camwa.2022.02.008
    - Preprint: arXiv, Hal

Works in Progress

  • I. Fontana, L.-M. Imbert-Gérard, A quasi-Trefftz space for the time-harmonic Maxwell's equation
    - In preparation.

  • I. Fontana, L.-M. Imbert-Gérard, Bessel-based approximation of variable-coefficient Helmholtz solutions.
    - In preparation.

  • K. Burns, I. Fontana, D. Lecoanet, G. Vasil, Analysis of tau spectrum for 1D eigenvalue problems.
    - In preparation.

  • I. Fontana, L.-M. Imbert-Gérard, S. Tordeaux, Existence, uniqueness, regularity result for time-harmonic first-order hyperbolic systems of Friedrichs type.
    - In preparation.

Thesis

  • I. Fontana, Interface Problems for Dam Modeling (Problèmes d'interface pour les ouvrages hydrauliques). Ph.D. Thesis
    - [Hal these]

Conference Talks & Seminars


Teaching

University of Arizona, 2024–present

  • Fall 2026: MATH 355: Analysis of Ordinary Differential Equations
  • Fall 2025: MATH/DATA 363: Introduction to Statistical Methods
    - Flipped course and co-teaching with Joseph Watkins
  • Fall 2024: MATH 122B: Calculus I

Northwestern University, 2023–2024

  • Winter 2023–Winter 2024: MATH 228-2: Multiple Integration and Vector Calculus
    - Taught four terms (six sections): Winter 2023 (2), Spring 2023, Fall 2023, Winter 2024 (2)
    - Course co-organized with Michael Miksis, Petia Vlahovska and Daniel Lecoanet

Outreach & Service

  • Seminar Co-organizer, University of Arizona, 2025–present
    - Co-organizer with faculty members of the “Modeling and Computation” weekly seminar in the Department of Mathematics
  • Math Postdoctoral President, University of Arizona, 2025–present
    - Organizer of the postdoc professional development seminar and other postdoc activities in the Department of Mathematics
  • Minisymposium Co-organizer, SIAM CSE25, March 2025
    - Co-organizer with Lise-Marie Imbert-Gérard of the minisymposium “Advances in Discontinuous Galerkin and Trefftz Methods” at the SIAM Conference on Computational Science and Engineering
  • WISE Mentor, University of Arizona, 2024–2025
    - Mentor for a Computer Science master’s student in the WISE mentorship program
  • Math Postdoctoral Vice-President, University of Arizona, 2024–2025
    - Vice-President in the governance of postdocs in the Department of Mathematics
  • Student Tutor, University of Udine, 2017–2018
    - Teaching assistance and outreach activities for Bachelor and Master degrees in Mathematics
  • Student Representative, University of Udine, 2014–2018
    - Student representative for Bachelor and Master degrees in Mathematics