A High-Accuracy Symplectic Scheme for a nonlinear transport problem
arXiv:2505.22022 · doi:10.1007/s40314-026-03668-7
Abstract
We analyze an advection-diffusion-reaction problem with non-homogeneous boundary conditions that models the chromatography process.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
33 pages, 5 Figures, 2 tables