Doubly Degenerate Parabolic Equation
Well-posedness and stability results motivated by Richards-type infiltration dynamics.
Read preprintModeling Flow in Porous Media, One Equation at a Time
I work on the mathematical analysis and finite element approximation of the Richards equation and higher-order extensions, with applications to infiltration and contaminant transport.
Selected Work
Bounded Auxiliary Variable FEM
Finite element formulation that improves robustness for highly nonlinear infiltration regimes.
Read preprintHeat Equation Animation
Visual walkthrough of diffusion in a sinusoidal channel using a finite element simulation.
Watch on Animations pageWelcome
I am a PhD candidate in Mathematics and Statistics at the University of Ottawa. My academic focus is on the theoretical and numerical analysis of infiltration models.
Specifically, I develop advanced numerical methods for the Richards equation and its higher-order extensions. This work models water infiltration in porous media to better predict pollutant movement and prevent groundwater contamination, incorporating both diffusion and dispersion effects.
Alongside my research, I am actively involved in mathematical education as a Teaching Assistant, a tutor at the Math Help Center, and through my visual project, "Abdo does maths", where I animate abstract mathematical concepts.