Garcke, Harald and Trautwein, Dennis (2022) Numerical analysis for a Cahn-Hilliard system modelling tumour growth with chemotaxis and active transport. JOURNAL OF NUMERICAL MATHEMATICS, 30 (4). pp. 295-324. ISSN 1570-2820, 1569-3953
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A diffuse interface model for tumour growth in the presence of a nutrient consumed by the tumour is considered. The system of equations consists of a Cahn-Hilliard equation with source terms for the tumour cells and a reaction-diffusion equation for the nutrient. We introduce a fully-discrete finite element approximation of the model and prove stability bounds for the discrete scheme. Moreover, we show that discrete solutions exist and depend continuously on the initial and boundary data. We then pass to the limit in the discretization parameters and prove convergence to a global-in-time weak solution to the model. Under additional assumptions, this weak solution is unique. Finally, we present some numerical results including numerical error investigation in one spatial dimension and some long time simulations in two and three spatial dimensions.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | FINITE-ELEMENT APPROXIMATION; DIFFUSE INTERFACE MODEL; DARCY MODEL; SIMULATION; EQUATION; SCHEMES; Cahn-Hilliard equation; diffuse interface model; tumour growth; chemotaxis; numerical analysis; finite element method; simulations |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Harald Garcke |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 14 Nov 2023 07:26 |
| Last Modified: | 14 Nov 2023 07:26 |
| URI: | https://pred.uni-regensburg.de/id/eprint/56633 |
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