A structure-preserving upwind DG scheme for a degenerate phase-field tumor model
arXiv:2304.09257 · doi:10.1016/j.camwa.2023.10.028
Abstract
In this work, we present a modification of the phase-field tumor growth model given in [26] that leads to bounded, more physically meaningful, volume fraction variables. In addition, we develop an upwind discontinuous Galerkin (DG) scheme preserving the mass conservation, pointwise bounds and energy stability of the continuous model. Finally, some computational tests in accordance with the theoretical results are introduced. In the first test, we compare our DG scheme with the finite element (FE) scheme related to the same time approximation. The DG scheme shows a well-behavior even for strong cross-diffusion effects in contrast with FE where numerical spurious oscillations appear. Moreover, the second test exhibits the behavior of the tumor-growth model under different choices of parameters and also of mobility and proliferation functions.
arXiv comment32 pages, 15 figures
References in corpus (7)
- Numerical Approximations for a three components Cahn-Hilliard phase-field Model based on the Invariant Energy Quadratization method
- Construction of arbitrary order finite element degree-of-freedom maps on polygonal and polyhedral cell meshes
- Mathematical models of Leukaemia and its treatment: A review
- An upwind DG scheme preserving the maximum principle for the convective Cahn-Hilliard model
- An unconditionally energy stable and positive upwind DG scheme for the Keller-Segel model
- A Glioblastoma PDE-ODE model including chemotaxis and vasculature
- Long-time Dynamics for a Cahn-Hilliard Tumor Growth Model with Chemotaxis