Unconditionally energy stable fully discrete schemes for a chemo-repulsion model
This work is devoted to studying unconditionally energy stable and mass-conservative numerical schemes for the following repulsive-productive chemotaxis model: find u ≥ 0, the cell density, and v ≥ 0, the chemical concentration, such that ∂tu − Δu −∇· (u∇v) = 0 in Ω, t> 0, ∂tv − Δv + v = u in Ω,...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión enviada para evaluación y publicación |
| Fecha de publicación: | 2019 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/89076 |
| Acceso en línea: | https://hdl.handle.net/11441/89076 https://doi.org/10.1090/mcom/3418 |
| Access Level: | acceso abierto |
| Palabra clave: | Chemorepulsion-production model Finite element approximation Unconditional energy-stability Quadratization of energy Regularization |
| Sumario: | This work is devoted to studying unconditionally energy stable and mass-conservative numerical schemes for the following repulsive-productive chemotaxis model: find u ≥ 0, the cell density, and v ≥ 0, the chemical concentration, such that ∂tu − Δu −∇· (u∇v) = 0 in Ω, t> 0, ∂tv − Δv + v = u in Ω, t> 0, in a bounded domain Ω ⊆ Rd, d = 2, 3. By using a regularization technique, we propose three fully discrete Finite Element (FE) approximations. The first one is a nonlinear approximation in the variables (u, v); the second one is another nonlinear approximation obtained by introducing σ = ∇v as an auxiliary variable; and the third one is a linear approximation constructed by mixing the regularization procedure with the energy quadratization technique, in which other auxiliary variables are introduced. In addition, we study the well-posedness of the numerical schemes, proving unconditional existence of solution, but conditional uniqueness (for the nonlinear schemes). Finally, we compare the behavior of such schemes throughout several numerical simulations and provide some conclusions. |
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