A High Accuracy Symplectic Scheme for Advection Diffusion Reaction Models in Bioseparation
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912669500440576 |
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| author | Siddiqua, Farjana Trenchea, Catalin |
| author_facet | Siddiqua, Farjana Trenchea, Catalin |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_22022 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A High Accuracy Symplectic Scheme for Advection Diffusion Reaction Models in Bioseparation Siddiqua, Farjana Trenchea, Catalin Numerical Analysis 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. |
| title | A High Accuracy Symplectic Scheme for Advection Diffusion Reaction Models in Bioseparation |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2505.22022 |