Research & CV

Numerical analysis, finite element methods, and mathematical modeling of flow and transport in porous media.

Education

Ph.D. in Mathematics and Statistics

09/2024 - Present
University of Ottawa, ON

Focus: Theoretical and numerical analysis of infiltration models (Richards equations) and higher-order extensions using Finite Element Methods.

Master's in Mathematics and Statistics

09/2023 - 09/2024
University of Ottawa, ON

Fast-tracked to Ph.D. program due to research excellence. Report: Theoretical and Numerical Analysis of Infiltration Models.

Bachelor's in Mathematics and Applications

09/2020 - 06/2023
Cadi Ayyad University, Marrakech, Morocco

Final-year project (Projet de fin d'etudes): "Principe du maximum et applications en analyse complexe." Read PDF

Publications

Mathematical analysis for a doubly degenerate parabolic equation: Application to the Richards equation

Submitted 02/2026
Benfanich, A., Bourgault, Y., & Beljadid, A. · Journal of Differential Equations

One-line summary: establishes well-posedness and stability results for a doubly degenerate parabolic model directly motivated by Richards-type infiltration dynamics.

arXiv Preprint PDF Journal Page DOI pending

A finite element method using a bounded auxiliary variable for solving the Richards equation

Submitted 09/2025
Benfanich, A., Bourgault, Y., & Beljadid, A. · Journal of Computational Physics

One-line summary: introduces an FEM formulation with an auxiliary bounded variable to improve numerical robustness in strongly nonlinear infiltration regimes.

arXiv Preprint PDF Journal Page DOI pending

Academic Experience

Research & Teaching Assistant

06/2023 - Present
University of Ottawa, ON
  • Conducting theoretical and numerical research on porous media flow for graduate programs.
  • Organize discussion groups, grade exams, and provide personalized academic support to students.

Math Help Center Tutor

Ongoing
University of Ottawa, ON

Provide drop-in support for students, facilitating collaborative learning and understanding of core concepts.

Conferences & Specialized Training

  • SIAM/CAIMS Joint Conference, Montreal (07/2025-08/2025): Delivered a talk on research findings as part of a mini-symposium.
  • Compute Ontario School (06/2025-07/2025): Applied machine learning concepts (Artificial Neural Networks) to computational problems.
  • Summer School in Mathematics, Queen's University (06/2024-07/2024): Intensive coursework on circulation models, reinforcement learning, Riemann surface topology, and SDEs.

Awards & Distinctions

  • Travel Scholarship (2025) - Awarded by the department to attend the SIAM/CAIMS Joint Conference in Montreal.
  • International Doctoral Scholarship (09/2024) - Awarded for research excellence.
  • Admission Scholarship (09/2024) - Awarded upon admission to the Ph.D. program.
  • Supervisor's Scholarship (2023-2024)
  • Partial Exemption Scholarship (2023-2024) - Merit-based exemption for international francophone students.