Work

Numerical Analysis of a Coupled 3D-1D Transport Problem

Year: 2026

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2603.19395

Authors: Taylor-LaPole, Alyssa, Gideon, Uzochi, Riviere, Beatrice, Vargun, Duygu

Institution: Rice University

Topic: Advanced Numerical Methods in Computational Mathematics

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, National Institutes of Health

Awards: RTG: Numerical Mathematics and Scientific Computing, Numerical methods for miscible displacement in coupled 3D-1D domains

OpenAlex ID: W7140107018

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