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Theoretical Convergence of Numerical Schemes for Coupled 3D-1D Partial Differential Equations

Published in Rice University, 2025

This paper analyzes numerical schemes for a steady state coupled 3D-1D diffusion-advection equations, establishing the existence and uniqueness of the weak solution and discrete solution, and some convergence results.

Recommended citation: Uzochi Gideon, MA Thesis. (2025). "Theoretical Convergence of Numerical Schemes for Coupled 3D-1D Partial Differential Equations." Rice University.
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Analysis of FEM methods for coupled 3D-1D diffusion-advection PDEs (Poster)

Published: October 04, 2024

Poster on numerical analysis of coupled PDEs with mixed dimensionality, presenting a finite element scheme with proven existence, uniqueness, and convergence.

Theoretical Convergence of Numerical Schemes for Coupled 3D-1D PDEs (Poster)

Published: September 27, 2025

Poster on discretizing coupled 3D-1D advection-diffusion PDEs using finite element and hybrid FEM–DG schemes with rigorous analysis of boundary conditions.

Formulation and Analysis of Numerical Schemes for Coupled 3D-1D PDEs

Published: October 03, 2025

Talk on modeling flows in porous media with 3D-1D coupled equations, using finite element and discontinuous Galerkin methods, with convergence, existence, and uniqueness analysis.

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Teaching, Phostine Premium Schools, 2022

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Teaching, Department of Computational & Applied Mathematics, Rice University, 2023

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