Ilaria Fontana

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

Publications

Articles and Conference Papers

• 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. Accepted in Forum Acusticum/Euronoise 2025, the 11th EAA Annual European Conference on Acoustics and Noise Control Engineering, 2025.
  - [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


• I. Fontana, D. A. Di Pietro, K. Kazymyrenko, A Posteriori Error Estimation via Equilibrated Stress Reconstruction for Unilateral Contact Problems. Presentations and videos to 10th International Conference on Adaptative Modeling and Simulation (ADMOS).
  - DOI: 10.23967/admos.2021.008.


• I. Fontana, K. Kazymyrenko, A interface model for dams with cohesive zone model coupling damage and plasticity. In preparation.


• I. Fontana, R. Vermiglio, An experimental investigation on weighted orthogonal polynomials for equations with infinite delay. 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

• Talk at ICOSAHOM 2025, The 15th International Conference on Spectral and High Order Methods, Quasi-Trefftz Spaces for Vector-Valued Equations, July 2025, Montréal (Canada)


• Talk at ADMOS 2025, 12th International Conference on Adaptive Modeling and Simulation, A Posteriori Error Analysis for Contact Problems with Application to Dam Modeling, June 2025, Barcelona (Spain)


• Talk at EFEF2025, 22nd European Finite Element Fair, Recent Advances on Quasi-Trefftz Methods Based on Generalized Plane Waves, May 2025, Trieste (Italy)


• Talk at CSE, SIAM Conference on Computational Science and Engineering, Quasi-Trefftz Methods with Applications to Maxwell's Equations, March 2025, Fort Worth, TX (USA)


• Analysis, Dynamics, and Applications Seminar in the Department of Mathematics at the University of Arizona, Analysis of the Tau Method for Eigenvalue Problems, November 2024, Tucson, AZ (USA)


• Modeling and Computation Seminar in the Department of Mathematics at the University of Arizona, A Posteriori Error Analysis for Contact Problems with Application to Dam Modeling, September 2024, Tucson, AZ (USA)


• Talk at WCCM-PANAC 2024, 16th World Congress on Computational Mechanics and 4th Pan American Congress on Computational Mechanics, Adaptive mesh algorithm for frictional contact problems based on a posteriori error analysis, July 2024, Vancouver (Canada)


• Talk at the Spring 2024 Finite Element Circus at Brown University, An equilibrated a posteriori error analysis for frictional contact problems, April 2024, Providence, RI (USA), [slides]

MATH/DATA 363: Introduction to Statistical Methods, University of Arizona

• Fall 2025: Co-teaching with Prof. Joseph C. Watkins; flipped course

MATH 122B: Calculus I, University of Arizona

• Fall 2024: Instructor for one section

MATH 228-2: Multiple Integration and Vector Calculus, Northwestern University

• Winter 2023: Instructor for two sections - Collaboration with Prof. Michael Miksis and Prof. Petia Vlahovska
• Spring 2023: Instructor for one section
• Fall 2023: Instructor for one section - Collaboration with Prof. Daniel Lecoanet
• Winter 2024: Instructor for two sections - Collaboration with Prof. Petia Vlahovska