Numerical Analysis of a Coupled 3D-1D Transport Problem
Numerical Analysis
2026-03-23 v1 Numerical Analysis
Analysis of PDEs
Abstract
A finite element solution coupled with an interior penalty discontinuous Galerkin solution are defined for the approximation of the coupled 3D-1D solute transport problem. Under sufficient regularity for the weak solutions, optimal error bounds are derived for the 3D concentration and 1D concentration, that are optimal with respect to the time step size and the mesh sizes. Numerical results verify the theoretical results.
Cite
@article{arxiv.2603.19395,
title = {Numerical Analysis of a Coupled 3D-1D Transport Problem},
author = {Alyssa Taylor-LaPole and Uzochi Gideon and Beatrice Riviere and Duygu Vargun},
journal= {arXiv preprint arXiv:2603.19395},
year = {2026}
}