Fully discrete positivity-preserving and energy-dissipating schemes for aggregation-diffusion equations with a gradient-flow structure
We propose fully discrete, implicit-in-time finite volume schemes for general nonlinear nonlocal Fokker-Planck type equations with a gradient flow structure, usually referred to as aggregation-diffusion equations, in any dimension. The schemes enjoy the positivity-preserving and energy-decaying prop...
| Main Authors: | , , |
|---|---|
| Format: | Journal article |
| Language: | English |
| Published: |
International Press
2020
|
| _version_ | 1797101398955917312 |
|---|---|
| author | Bailo, R Carrillo de la Plata, JA Hu, J |
| author_facet | Bailo, R Carrillo de la Plata, JA Hu, J |
| author_sort | Bailo, R |
| collection | OXFORD |
| description | We propose fully discrete, implicit-in-time finite volume schemes for general nonlinear nonlocal Fokker-Planck type equations with a gradient flow structure, usually referred to as aggregation-diffusion equations, in any dimension. The schemes enjoy the positivity-preserving and energy-decaying properties, essential for their practical use. The first order in time and space scheme unconditionally verifies these properties for general nonlinear diffusion and interaction potentials while the second order scheme does so provided a CFL condition holds. Dimensional splitting allows for the construction of these schemes with the same properties and a reduced computational cost in higher dimensions. Numerical experiments validate the schemes and show their ability to handle complicated phenomena in aggregation-diffusion equations such as free boundaries, metastability, merging and phase transitions. |
| first_indexed | 2024-03-07T05:51:21Z |
| format | Journal article |
| id | oxford-uuid:e8fd7d96-3b0b-4fb7-a198-f37323f14ad4 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T05:51:21Z |
| publishDate | 2020 |
| publisher | International Press |
| record_format | dspace |
| spelling | oxford-uuid:e8fd7d96-3b0b-4fb7-a198-f37323f14ad42022-03-27T10:51:00ZFully discrete positivity-preserving and energy-dissipating schemes for aggregation-diffusion equations with a gradient-flow structureJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:e8fd7d96-3b0b-4fb7-a198-f37323f14ad4EnglishSymplectic ElementsInternational Press2020Bailo, RCarrillo de la Plata, JAHu, JWe propose fully discrete, implicit-in-time finite volume schemes for general nonlinear nonlocal Fokker-Planck type equations with a gradient flow structure, usually referred to as aggregation-diffusion equations, in any dimension. The schemes enjoy the positivity-preserving and energy-decaying properties, essential for their practical use. The first order in time and space scheme unconditionally verifies these properties for general nonlinear diffusion and interaction potentials while the second order scheme does so provided a CFL condition holds. Dimensional splitting allows for the construction of these schemes with the same properties and a reduced computational cost in higher dimensions. Numerical experiments validate the schemes and show their ability to handle complicated phenomena in aggregation-diffusion equations such as free boundaries, metastability, merging and phase transitions. |
| spellingShingle | Bailo, R Carrillo de la Plata, JA Hu, J Fully discrete positivity-preserving and energy-dissipating schemes for aggregation-diffusion equations with a gradient-flow structure |
| title | Fully discrete positivity-preserving and energy-dissipating schemes for aggregation-diffusion equations with a gradient-flow structure |
| title_full | Fully discrete positivity-preserving and energy-dissipating schemes for aggregation-diffusion equations with a gradient-flow structure |
| title_fullStr | Fully discrete positivity-preserving and energy-dissipating schemes for aggregation-diffusion equations with a gradient-flow structure |
| title_full_unstemmed | Fully discrete positivity-preserving and energy-dissipating schemes for aggregation-diffusion equations with a gradient-flow structure |
| title_short | Fully discrete positivity-preserving and energy-dissipating schemes for aggregation-diffusion equations with a gradient-flow structure |
| title_sort | fully discrete positivity preserving and energy dissipating schemes for aggregation diffusion equations with a gradient flow structure |
| work_keys_str_mv | AT bailor fullydiscretepositivitypreservingandenergydissipatingschemesforaggregationdiffusionequationswithagradientflowstructure AT carrillodelaplataja fullydiscretepositivitypreservingandenergydissipatingschemesforaggregationdiffusionequationswithagradientflowstructure AT huj fullydiscretepositivitypreservingandenergydissipatingschemesforaggregationdiffusionequationswithagradientflowstructure |