A high-accuracy symplectic scheme for a nonlinear transport problem
Farjana Siddiqua, Catalin Trenchea
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Source: Crossref
Published: Apr 21, 2026
DOI: 10.1007/s40314-026-03668-7
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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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