A High Accuracy Symplectic Scheme for Advection Diffusion Reaction Models in Bioseparation

TL;DR

This paper develops and analyzes a high-accuracy symplectic scheme combining implicit midpoint and finite element methods for advection-diffusion-reaction models in bioseparation, ensuring stability and error control.

Contribution

It introduces a novel symplectic scheme for complex bioseparation models with rigorous stability and error analysis for both linear and nonlinear adsorption cases.

Findings

The scheme is stable for constant and affine adsorption.

Error estimates are established for semi-discrete and fully discrete cases.

Numerical tests confirm the theoretical stability and accuracy.

Abstract

We analyze an advection-diffusion-reaction problem with non-homogeneous boundary conditions that models the chromatography process, a vital stage in bioseparation. We prove stability and error estimates for both constant and affine adsorption, using the symplectic one-step implicit midpoint method for time discretization and finite elements for spatial discretization. In addition, we perform the stability analysis for the nonlinear, explicit adsorption in the continuous and semi-discrete cases. For the nonlinear, explicit adsorption, we also complete the error analysis for the semi-discrete case and prove the existence of a solution for the fully discrete case. The numerical tests validate our theoretical results.