Structure-preserving local discontinuous Galerkin discretization of conformational conversion systems
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866910235534295040 |
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| author | Antonietti, Paola F. Corti, Mattia Gómez, Sergio Perugia, Ilaria |
| author_facet | Antonietti, Paola F. Corti, Mattia Gómez, Sergio Perugia, Ilaria |
| contents | We investigate a two-state conformational conversion system and introduce a novel structure-preserving numerical scheme that couples a local discontinuous Galerkin space discretization with the backward Euler time-integration method. The model is first reformulated in terms of auxiliary variables involving suitable nonlinear transformations, which allow us to enforce positivity and boundedness at the numerical level. Then, we prove a discrete entropy-stability inequality, which we use to show the existence of discrete solutions, as well as to establish the convergence of the scheme by means of some discrete compactness arguments. As a by-product of the theoretical analysis, we also prove the existence of global weak solutions satisfying the system's physical bounds. Numerical results validate the theoretical results and assess the capabilities of the proposed method in practice. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_04830 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Structure-preserving local discontinuous Galerkin discretization of conformational conversion systems Antonietti, Paola F. Corti, Mattia Gómez, Sergio Perugia, Ilaria Numerical Analysis 65M60, 65M12, 35K57, 35Q92 We investigate a two-state conformational conversion system and introduce a novel structure-preserving numerical scheme that couples a local discontinuous Galerkin space discretization with the backward Euler time-integration method. The model is first reformulated in terms of auxiliary variables involving suitable nonlinear transformations, which allow us to enforce positivity and boundedness at the numerical level. Then, we prove a discrete entropy-stability inequality, which we use to show the existence of discrete solutions, as well as to establish the convergence of the scheme by means of some discrete compactness arguments. As a by-product of the theoretical analysis, we also prove the existence of global weak solutions satisfying the system's physical bounds. Numerical results validate the theoretical results and assess the capabilities of the proposed method in practice. |
| title | Structure-preserving local discontinuous Galerkin discretization of conformational conversion systems |
| topic | Numerical Analysis 65M60, 65M12, 35K57, 35Q92 |
| url | https://arxiv.org/abs/2511.04830 |