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arXiv · 2505.22022

A High-Accuracy Symplectic Scheme for a nonlinear transport problem

Farjana Siddiqua·Catalin Trenchea
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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

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Farjana Siddiqua, Catalin Trenchea. 2025-05-28. A High-Accuracy Symplectic Scheme for a nonlinear transport problem. https://doi.org/10.1007/s40314-026-03668-7

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