Study of a chemo-repulsion model with quadratic production. Part II: Analysis of an unconditionally energy-stable fully discrete scheme

This work is devoted to the study of a fully discrete scheme for a repulsive chemotaxis with quadratic production model. By following the ideas presented in Guillén-González et al. (2020), we introduce an auxiliary variable (the gradient of the chemical concentration), and prove that the correspondi...

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Autores: Guillén González, Francisco Manuel, Rodríguez Bellido, María Ángeles, Rueda Gómez, Diego A.
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2020
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:dnet:idus________::a3b9234313c00c4cad2f035b8ccae850
Acceso en línea:https://hdl.handle.net/11441/186555
https://doi.org/10.1016/j.camwa.2020.04.010
Access Level:acceso abierto
Palabra clave:Chemorepulsion–production model
Fully discrete scheme
Finite element method
Energy-stability
Convergence
Error estimates
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spelling Study of a chemo-repulsion model with quadratic production. Part II: Analysis of an unconditionally energy-stable fully discrete schemeGuillén González, Francisco ManuelRodríguez Bellido, María ÁngelesRueda Gómez, Diego A.Chemorepulsion–production modelFully discrete schemeFinite element methodEnergy-stabilityConvergenceError estimatesThis work is devoted to the study of a fully discrete scheme for a repulsive chemotaxis with quadratic production model. By following the ideas presented in Guillén-González et al. (2020), we introduce an auxiliary variable (the gradient of the chemical concentration), and prove that the corresponding Finite Element (FE) backward Euler scheme is conservative and unconditionally energy-stable. Additionally, we also study some properties like solvability, a priori estimates, convergence towards weak solutions and error estimates. On the other hand, we propose two linear iterative methods to approach the nonlinear scheme: an energy-stable Picard method and Newton’s method. We prove solvability and convergence of both methods towards the nonlinear scheme. Finally, we provide some numerical results in agreement with our theoretical analysis with respect to the error estimates.ElsevierEcuaciones Diferenciales y Análisis NuméricoFQM131: Ecuaciones diferenciales, Simulación Num. y Desarrollo Software2020info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfapplication/pdfhttps://hdl.handle.net/11441/186555https://doi.org/10.1016/j.camwa.2020.04.010reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésComputers & Mathematics with Applications, 80 (5), 636-652. 10.1016/j.camwa.2020.04.010info:eu-repo/semantics/openAccessoai:dnet:idus________::a3b9234313c00c4cad2f035b8ccae8502026-06-17T12:51:07Z
dc.title.none.fl_str_mv Study of a chemo-repulsion model with quadratic production. Part II: Analysis of an unconditionally energy-stable fully discrete scheme
title Study of a chemo-repulsion model with quadratic production. Part II: Analysis of an unconditionally energy-stable fully discrete scheme
spellingShingle Study of a chemo-repulsion model with quadratic production. Part II: Analysis of an unconditionally energy-stable fully discrete scheme
Guillén González, Francisco Manuel
Chemorepulsion–production model
Fully discrete scheme
Finite element method
Energy-stability
Convergence
Error estimates
title_short Study of a chemo-repulsion model with quadratic production. Part II: Analysis of an unconditionally energy-stable fully discrete scheme
title_full Study of a chemo-repulsion model with quadratic production. Part II: Analysis of an unconditionally energy-stable fully discrete scheme
title_fullStr Study of a chemo-repulsion model with quadratic production. Part II: Analysis of an unconditionally energy-stable fully discrete scheme
title_full_unstemmed Study of a chemo-repulsion model with quadratic production. Part II: Analysis of an unconditionally energy-stable fully discrete scheme
title_sort Study of a chemo-repulsion model with quadratic production. Part II: Analysis of an unconditionally energy-stable fully discrete scheme
dc.creator.none.fl_str_mv Guillén González, Francisco Manuel
Rodríguez Bellido, María Ángeles
Rueda Gómez, Diego A.
author Guillén González, Francisco Manuel
author_facet Guillén González, Francisco Manuel
Rodríguez Bellido, María Ángeles
Rueda Gómez, Diego A.
author_role author
author2 Rodríguez Bellido, María Ángeles
Rueda Gómez, Diego A.
author2_role author
author
dc.contributor.none.fl_str_mv Ecuaciones Diferenciales y Análisis Numérico
FQM131: Ecuaciones diferenciales, Simulación Num. y Desarrollo Software
dc.subject.none.fl_str_mv Chemorepulsion–production model
Fully discrete scheme
Finite element method
Energy-stability
Convergence
Error estimates
topic Chemorepulsion–production model
Fully discrete scheme
Finite element method
Energy-stability
Convergence
Error estimates
description This work is devoted to the study of a fully discrete scheme for a repulsive chemotaxis with quadratic production model. By following the ideas presented in Guillén-González et al. (2020), we introduce an auxiliary variable (the gradient of the chemical concentration), and prove that the corresponding Finite Element (FE) backward Euler scheme is conservative and unconditionally energy-stable. Additionally, we also study some properties like solvability, a priori estimates, convergence towards weak solutions and error estimates. On the other hand, we propose two linear iterative methods to approach the nonlinear scheme: an energy-stable Picard method and Newton’s method. We prove solvability and convergence of both methods towards the nonlinear scheme. Finally, we provide some numerical results in agreement with our theoretical analysis with respect to the error estimates.
publishDate 2020
dc.date.none.fl_str_mv 2020
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv https://hdl.handle.net/11441/186555
https://doi.org/10.1016/j.camwa.2020.04.010
url https://hdl.handle.net/11441/186555
https://doi.org/10.1016/j.camwa.2020.04.010
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Computers & Mathematics with Applications, 80 (5), 636-652.
10.1016/j.camwa.2020.04.010
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 Elsevier
publisher.none.fl_str_mv Elsevier
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 15,812429

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