Details
| Original language | English |
|---|---|
| Article number | 112711 |
| Journal | Journal of computational physics |
| Volume | 499 |
| Early online date | 14 Dec 2023 |
| Publication status | Published - 15 Feb 2024 |
Abstract
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 P1 or Q1 finite elements to discretize the model in space and the θ-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.
Keywords
- Cancer invasion, Cross-diffusion equation, Existence of solutions, FEM-FCT stabilization, Positivity preservation
ASJC Scopus subject areas
- Mathematics(all)
- Numerical Analysis
- Mathematics(all)
- Modelling and Simulation
- Physics and Astronomy(all)
- Physics and Astronomy (miscellaneous)
- Physics and Astronomy(all)
- Computer Science(all)
- Computer Science Applications
- Mathematics(all)
- Computational Mathematics
- Mathematics(all)
- Applied Mathematics
Sustainable Development Goals
Cite this
- Standard
- Harvard
- Apa
- Vancouver
- BibTeX
- RIS
In: Journal of computational physics, Vol. 499, 112711, 15.02.2024.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Flux-corrected transport stabilization of an evolutionary cross-diffusion cancer invasion model
AU - Heydari, Shahin
AU - Knobloch, Petr
AU - Wick, Thomas
N1 - Funding Information: This work was initiated during a research stay of the first author at the Institute of Applied Mathematics at the Leibniz University Hanover from November 2021 to April 2022 for which hospitality is still gratefully acknowledged. The work of Shahin Heydari was further supported through the grant No. 396921 of the Charles University Grant Agency and the grant SVV-2023-260711 of Charles University . The work of Petr Knobloch was supported through the grant No. 22-01591S of the Czech Science Foundation .
PY - 2024/2/15
Y1 - 2024/2/15
N2 - 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 P1 or Q1 finite elements to discretize the model in space and the θ-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.
AB - 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 P1 or Q1 finite elements to discretize the model in space and the θ-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.
KW - Cancer invasion
KW - Cross-diffusion equation
KW - Existence of solutions
KW - FEM-FCT stabilization
KW - Positivity preservation
UR - http://www.scopus.com/inward/record.url?scp=85185827631&partnerID=8YFLogxK
U2 - 10.48550/arXiv.2307.08096
DO - 10.48550/arXiv.2307.08096
M3 - Article
AN - SCOPUS:85185827631
VL - 499
JO - Journal of computational physics
JF - Journal of computational physics
SN - 0021-9991
M1 - 112711
ER -