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.

翻译：本文分析了一个具有非齐次边界条件的平流-扩散-反应问题，该问题模拟了生物分离中关键步骤——色谱过程。针对常系数与仿射吸附情形，我们采用时间离散的辛单步隐式中点方法与空间离散的有限元方法，证明了稳定性与误差估计。此外，我们对非线性显式吸附情形在连续与半离散情况下进行了稳定性分析。对于非线性显式吸附，我们还完成了半离散情形的误差分析，并证明了全离散情形解的存在性。数值实验验证了我们的理论结果。