Xhahysa, S. (2024). Finite-volume approximation of cross-diffusion systems for tumor growth. In Frontiers in Interacting Particle Systems, Aggregation-Diffusion Equations and Collective Behavior 2024 (pp. 46–46).
We present an implicit Euler finite volume scheme for the mechanical tumor growth model proposed by Jackson and Byrne. The model comprises a cross-diffusion system with no-flux boundary conditions. The numerical scheme preserves the formal gradient-flow or entropy structure and meets the requirements for the boundedness-by-entropy method. We prove the existence of discrete solutions and the convergence of the numerical scheme.
