Flux-corrected transport stabilization of an evolutionary cross-diffusion cancer invasion model

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F24%3A10489228" target="_blank" >RIV/00216208:11320/24:10489228 - isvavai.cz</a>

Výsledek na webu

<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=QcD_SxhfpL" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=QcD_SxhfpL</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.jcp.2023.112711" target="_blank" >10.1016/j.jcp.2023.112711</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Flux-corrected transport stabilization of an evolutionary cross-diffusion cancer invasion model

Popis výsledku v původním jazyce

In the present work, we investigate a model of the invasion of healthy tissue by cancer cells which is described by a system of nonlinear PDEs consisting of a cross-diffusion-reaction equation and two additional nonlinear ordinary differential equations. We show that when the convective part of the system, the haptotaxis term, is dominant, then straightforward numerical methods for the studied system may be unstable. We present an implicit finite element method using conforming P-1 or Q(1) finite elements to discretize the model in space and the theta-method for discretization in time. The discrete problem is stabilized using a nonlinear flux-corrected transport approach. It is proved that both the nonlinear scheme and the linearized problems used in fixed-point iterations are solvable and positivity preserving. Several numerical experiments are presented in 2D to demonstrate the performance of the proposed method.

Název v anglickém jazyce

Flux-corrected transport stabilization of an evolutionary cross-diffusion cancer invasion model

Popis výsledku anglicky

In the present work, we investigate a model of the invasion of healthy tissue by cancer cells which is described by a system of nonlinear PDEs consisting of a cross-diffusion-reaction equation and two additional nonlinear ordinary differential equations. We show that when the convective part of the system, the haptotaxis term, is dominant, then straightforward numerical methods for the studied system may be unstable. We present an implicit finite element method using conforming P-1 or Q(1) finite elements to discretize the model in space and the theta-method for discretization in time. The discrete problem is stabilized using a nonlinear flux-corrected transport approach. It is proved that both the nonlinear scheme and the linearized problems used in fixed-point iterations are solvable and positivity preserving. Several numerical experiments are presented in 2D to demonstrate the performance of the proposed method.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

<a href="/cs/project/GA22-01591S" target="_blank" >GA22-01591S: Matematická teorie a numerická analýza rovnic vazkých newtonovských stlačitelných tekutin</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2024

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Journal of Computational Physics

ISSN

0021-9991

e-ISSN

1090-2716

Svazek periodika

499

Číslo periodika v rámci svazku

15 February 2024

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

19

Strana od-do

112711

Kód UT WoS článku

001142100200001

EID výsledku v databázi Scopus

2-s2.0-85185827631