Numerical Analysis of a Coupled 3D-1D Transport Problem
This work addresses a domain-specific transport modeling problem, likely incremental as it builds on existing numerical methods.
The authors tackled the coupled 3D-1D solute transport problem by developing a finite element method combined with an interior penalty discontinuous Galerkin solution, deriving optimal error bounds for both 3D and 1D concentrations with respect to time step and mesh sizes, and verifying these results numerically.
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.