RT journal article
T1 A structure-preserving upwind DG scheme for a degenerate phase-field tumor model
A1 Acosta Soba, Daniel
A1 Guillén González, Francisco
A1 Rodríguez Galván, José Rafael
A2 Matemáticas
K1 Degenerate Cahn-Hilliard
K1 Degenerate proliferation
K1 Cross-diffusion
K1 Discrete pointwise bounds
K1 Discrete energy stability
AB 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 DGschemeshows awell-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.
SN 0898-1221
YR 2023
FD 2023-10-23
LK http://hdl.handle.net/10498/32253
UL http://hdl.handle.net/10498/32253
LA eng
DS Repositorio Institucional de la Universidad de Cádiz
RD 21-sep-2026