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

Result code in 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>
Result on the web
<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>

Result language
angličtina
Original language name
Flux-corrected transport stabilization of an evolutionary cross-diffusion cancer invasion model
Original language description
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.
Czech name
—
Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10102 - Applied mathematics

Project
<a href="/en/project/GA22-01591S" target="_blank" >GA22-01591S: Mathematical theory and numerical analysis for equations of viscous newtonian compressible fluids</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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