Convergence of a finite volume scheme for a system of interacting species with cross-diffusion
In this work we present the convergence of a positivity preserving semi-discrete finite volume scheme for a coupled system of two non-local partial differential equations with cross-diffusion. The key to proving the convergence result is to establish positivity in order to obtain a discrete energy e...
| Váldodahkkit: | , , |
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| Materiálatiipa: | Journal article |
| Giella: | English |
| Almmustuhtton: |
Springer Verlag
2020
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| _version_ | 1826281007363391488 |
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| author | Carrillo de la Plata, J Filbet, F Schmidtchen, M |
| author_facet | Carrillo de la Plata, J Filbet, F Schmidtchen, M |
| author_sort | Carrillo de la Plata, J |
| collection | OXFORD |
| description | In this work we present the convergence of a positivity preserving semi-discrete finite volume scheme for a coupled system of two non-local partial differential equations with cross-diffusion. The key to proving the convergence result is to establish positivity in order to obtain a discrete energy estimate to obtain compactness. We numerically observe the convergence to reference solutions with a first order accuracy in space. Moreover we recover segregated stationary states in spite of the regularising effect of the self-diffusion. However, if the self-diffusion or the cross-diffusion is strong enough, mixing occurs while both densities remain continuous. |
| first_indexed | 2024-03-07T00:22:18Z |
| format | Journal article |
| id | oxford-uuid:7cf911f2-1f40-499b-85d6-9e60e8bdbc4c |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T00:22:18Z |
| publishDate | 2020 |
| publisher | Springer Verlag |
| record_format | dspace |
| spelling | oxford-uuid:7cf911f2-1f40-499b-85d6-9e60e8bdbc4c2022-03-26T21:00:23ZConvergence of a finite volume scheme for a system of interacting species with cross-diffusionJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:7cf911f2-1f40-499b-85d6-9e60e8bdbc4cEnglishSymplectic ElementsSpringer Verlag2020Carrillo de la Plata, JFilbet, FSchmidtchen, MIn this work we present the convergence of a positivity preserving semi-discrete finite volume scheme for a coupled system of two non-local partial differential equations with cross-diffusion. The key to proving the convergence result is to establish positivity in order to obtain a discrete energy estimate to obtain compactness. We numerically observe the convergence to reference solutions with a first order accuracy in space. Moreover we recover segregated stationary states in spite of the regularising effect of the self-diffusion. However, if the self-diffusion or the cross-diffusion is strong enough, mixing occurs while both densities remain continuous. |
| spellingShingle | Carrillo de la Plata, J Filbet, F Schmidtchen, M Convergence of a finite volume scheme for a system of interacting species with cross-diffusion |
| title | Convergence of a finite volume scheme for a system of interacting species with cross-diffusion |
| title_full | Convergence of a finite volume scheme for a system of interacting species with cross-diffusion |
| title_fullStr | Convergence of a finite volume scheme for a system of interacting species with cross-diffusion |
| title_full_unstemmed | Convergence of a finite volume scheme for a system of interacting species with cross-diffusion |
| title_short | Convergence of a finite volume scheme for a system of interacting species with cross-diffusion |
| title_sort | convergence of a finite volume scheme for a system of interacting species with cross diffusion |
| work_keys_str_mv | AT carrillodelaplataj convergenceofafinitevolumeschemeforasystemofinteractingspecieswithcrossdiffusion AT filbetf convergenceofafinitevolumeschemeforasystemofinteractingspecieswithcrossdiffusion AT schmidtchenm convergenceofafinitevolumeschemeforasystemofinteractingspecieswithcrossdiffusion |