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

TL;DR

This paper develops a finite element and discontinuous Galerkin method for a coupled 3D-1D solute transport problem, deriving optimal error bounds and validating them through numerical experiments.

Contribution

It introduces a novel coupled finite element and interior penalty discontinuous Galerkin approach with proven optimal error estimates for 3D-1D transport models.

Findings

Optimal error bounds for 3D and 1D concentrations.

Numerical results confirm theoretical error estimates.

Method achieves high accuracy under regularity assumptions.

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.