Bound-preserving finite element approximations of the Keller-Segel equations

This paper aims to develop numerical approximations of the Keller{Segel equations that mimic at the discrete level the lower bounds and the energy law of the continuous problem. We solve these equations for two unknowns: the organism (or cell) density, which is a positive variable, and the chemoattr...

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Detalles Bibliográficos
Autores: Badia, Santiago, Bonilla, Jesús, Gutiérrez Santacreu, Juan Vicente
Tipo de recurso: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2023
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/168309
Acceso en línea:https://hdl.handle.net/11441/168309
https://doi.org/10.1142/S0218202523500148
Access Level:acceso abierto
Palabra clave:Keller-Segel equations
Nonlinear parabolic equations
Shock detector
Lower bounds
Energy law
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spelling Bound-preserving finite element approximations of the Keller-Segel equationsBadia, SantiagoBonilla, JesúsGutiérrez Santacreu, Juan VicenteKeller-Segel equationsNonlinear parabolic equationsShock detectorLower boundsEnergy lawThis paper aims to develop numerical approximations of the Keller{Segel equations that mimic at the discrete level the lower bounds and the energy law of the continuous problem. We solve these equations for two unknowns: the organism (or cell) density, which is a positive variable, and the chemoattractant density, which is a non-negative variable. We propose two algorithms, which combine a stabilized nite element method and a semi-implicit time integration. The stabilization consists of a nonlinear arti cial di usion that employs a graph-Laplacian operator and a shock detector that localizes local extrema. As a result, both algorithms turn out to be nonlinear and can generate cell and chemoattractant numerical densities ful lling lower bounds. However, the rst algorithm requires a suitable constraint between the space and time discrete parameters, whereas the second one does not. We design the latter to attain a discrete energy law on acute meshes.World Scientific Public.Matemática Aplicada I2023info:eu-repo/semantics/articleinfo:eu-repo/semantics/acceptedVersionapplication/pdfapplication/pdfhttps://hdl.handle.net/11441/168309https://doi.org/10.1142/S0218202523500148reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésMathematical Models and Methods in Applied Sciences, 33 (3), 609-642.https://www.worldscientific.com/doi/10.1142/S0218202523500148info:eu-repo/semantics/openAccessoai:idus.us.es:11441/1683092026-06-17T12:51:07Z
dc.title.none.fl_str_mv Bound-preserving finite element approximations of the Keller-Segel equations
title Bound-preserving finite element approximations of the Keller-Segel equations
spellingShingle Bound-preserving finite element approximations of the Keller-Segel equations
Badia, Santiago
Keller-Segel equations
Nonlinear parabolic equations
Shock detector
Lower bounds
Energy law
title_short Bound-preserving finite element approximations of the Keller-Segel equations
title_full Bound-preserving finite element approximations of the Keller-Segel equations
title_fullStr Bound-preserving finite element approximations of the Keller-Segel equations
title_full_unstemmed Bound-preserving finite element approximations of the Keller-Segel equations
title_sort Bound-preserving finite element approximations of the Keller-Segel equations
dc.creator.none.fl_str_mv Badia, Santiago
Bonilla, Jesús
Gutiérrez Santacreu, Juan Vicente
author Badia, Santiago
author_facet Badia, Santiago
Bonilla, Jesús
Gutiérrez Santacreu, Juan Vicente
author_role author
author2 Bonilla, Jesús
Gutiérrez Santacreu, Juan Vicente
author2_role author
author
dc.contributor.none.fl_str_mv Matemática Aplicada I
dc.subject.none.fl_str_mv Keller-Segel equations
Nonlinear parabolic equations
Shock detector
Lower bounds
Energy law
topic Keller-Segel equations
Nonlinear parabolic equations
Shock detector
Lower bounds
Energy law
description This paper aims to develop numerical approximations of the Keller{Segel equations that mimic at the discrete level the lower bounds and the energy law of the continuous problem. We solve these equations for two unknowns: the organism (or cell) density, which is a positive variable, and the chemoattractant density, which is a non-negative variable. We propose two algorithms, which combine a stabilized nite element method and a semi-implicit time integration. The stabilization consists of a nonlinear arti cial di usion that employs a graph-Laplacian operator and a shock detector that localizes local extrema. As a result, both algorithms turn out to be nonlinear and can generate cell and chemoattractant numerical densities ful lling lower bounds. However, the rst algorithm requires a suitable constraint between the space and time discrete parameters, whereas the second one does not. We design the latter to attain a discrete energy law on acute meshes.
publishDate 2023
dc.date.none.fl_str_mv 2023
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/acceptedVersion
format article
status_str acceptedVersion
dc.identifier.none.fl_str_mv https://hdl.handle.net/11441/168309
https://doi.org/10.1142/S0218202523500148
url https://hdl.handle.net/11441/168309
https://doi.org/10.1142/S0218202523500148
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Mathematical Models and Methods in Applied Sciences, 33 (3), 609-642.
https://www.worldscientific.com/doi/10.1142/S0218202523500148
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv World Scientific Public.
publisher.none.fl_str_mv World Scientific Public.
dc.source.none.fl_str_mv reponame:idUS. Depósito de Investigación de la Universidad de Sevilla
instname:Universidad de Sevilla (US)
instname_str Universidad de Sevilla (US)
reponame_str idUS. Depósito de Investigación de la Universidad de Sevilla
collection idUS. Depósito de Investigación de la Universidad de Sevilla
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,811543

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