Finite element approximation and very weak solution existence in a two-dimensional, degenerate Keller-Segel model

This paper is devoted to the design and analysis of a numerical algorithm for approximating solutions of a degenerate cross-diffusion system, which models particular instances of taxis-type migration processes under local sensing mechanisms. The degeneracy leads to solutions that are very weak due t...

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Autor: Gutiérrez Santacreu, Juan Vicente
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2026
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:dnet:idus________::acb60e392eaaf0ac12edaa8bee83ff94
Acceso en línea:https://hdl.handle.net/11441/186812
https://doi.org/10.1007/s10915-026-03245-4
Access Level:acceso abierto
Palabra clave:Degenerate Keller–Segel equations
Very weak solutions
Finite-element approximation
Convergence analysis
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spelling Finite element approximation and very weak solution existence in a two-dimensional, degenerate Keller-Segel modelGutiérrez Santacreu, Juan VicenteDegenerate Keller–Segel equationsVery weak solutionsFinite-element approximationConvergence analysisThis paper is devoted to the design and analysis of a numerical algorithm for approximating solutions of a degenerate cross-diffusion system, which models particular instances of taxis-type migration processes under local sensing mechanisms. The degeneracy leads to solutions that are very weak due to the low regularity themselves. Specifically, the solutions satisfy pointwise bounds (such as positivity and the maximum principle), integrability (such as mass conservation), and dual a priori estimates. The proposed numerical scheme combines a finite element spatial discretization with Euler time stepping. The discrete solutions preserve the above-mentioned properties at the discrete level, enabling the derivation of compactness arguments and the convergence (up to a subsequence) of the numerical solutions to a very weak solution of the continuous problem on two-dimensional polygonal domains.SpringerMatemática Aplicada IFQM131: Ecuaciones diferenciales, Simulación Num. y Desarrollo SoftwareUniversidad de Sevilla2026info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfapplication/pdfhttps://hdl.handle.net/11441/186812https://doi.org/10.1007/s10915-026-03245-4reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésJournal of Scientific Computing, 107, 38. https://link.springer.com/article/10.1007/s10915-026-03245-4info:eu-repo/semantics/openAccessoai:dnet:idus________::acb60e392eaaf0ac12edaa8bee83ff942026-06-17T12:51:07Z
dc.title.none.fl_str_mv Finite element approximation and very weak solution existence in a two-dimensional, degenerate Keller-Segel model
title Finite element approximation and very weak solution existence in a two-dimensional, degenerate Keller-Segel model
spellingShingle Finite element approximation and very weak solution existence in a two-dimensional, degenerate Keller-Segel model
Gutiérrez Santacreu, Juan Vicente
Degenerate Keller–Segel equations
Very weak solutions
Finite-element approximation
Convergence analysis
title_short Finite element approximation and very weak solution existence in a two-dimensional, degenerate Keller-Segel model
title_full Finite element approximation and very weak solution existence in a two-dimensional, degenerate Keller-Segel model
title_fullStr Finite element approximation and very weak solution existence in a two-dimensional, degenerate Keller-Segel model
title_full_unstemmed Finite element approximation and very weak solution existence in a two-dimensional, degenerate Keller-Segel model
title_sort Finite element approximation and very weak solution existence in a two-dimensional, degenerate Keller-Segel model
dc.creator.none.fl_str_mv Gutiérrez Santacreu, Juan Vicente
author Gutiérrez Santacreu, Juan Vicente
author_facet Gutiérrez Santacreu, Juan Vicente
author_role author
dc.contributor.none.fl_str_mv Matemática Aplicada I
FQM131: Ecuaciones diferenciales, Simulación Num. y Desarrollo Software
Universidad de Sevilla
dc.subject.none.fl_str_mv Degenerate Keller–Segel equations
Very weak solutions
Finite-element approximation
Convergence analysis
topic Degenerate Keller–Segel equations
Very weak solutions
Finite-element approximation
Convergence analysis
description This paper is devoted to the design and analysis of a numerical algorithm for approximating solutions of a degenerate cross-diffusion system, which models particular instances of taxis-type migration processes under local sensing mechanisms. The degeneracy leads to solutions that are very weak due to the low regularity themselves. Specifically, the solutions satisfy pointwise bounds (such as positivity and the maximum principle), integrability (such as mass conservation), and dual a priori estimates. The proposed numerical scheme combines a finite element spatial discretization with Euler time stepping. The discrete solutions preserve the above-mentioned properties at the discrete level, enabling the derivation of compactness arguments and the convergence (up to a subsequence) of the numerical solutions to a very weak solution of the continuous problem on two-dimensional polygonal domains.
publishDate 2026
dc.date.none.fl_str_mv 2026
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/11441/186812
https://doi.org/10.1007/s10915-026-03245-4
url https://hdl.handle.net/11441/186812
https://doi.org/10.1007/s10915-026-03245-4
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Journal of Scientific Computing, 107, 38.
https://link.springer.com/article/10.1007/s10915-026-03245-4
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 Springer
publisher.none.fl_str_mv Springer
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 15,81155

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