A structure-preserving upwind DG scheme for a degenerate phase-field tumor model.

In this work, we present a modification of the phase-field tumor growth model given in [1] 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. • Extension of phase-field tumor model to be pointwise bounded and energy-dissipative. • Development of DG scheme that preserves the pointwise bounds and is energy-stable. • Numerical experiments contrasting the DG approximation with a FE counterpart. • Simulations showing the effects of different mobility and proliferation functions. [ABSTRACT FROM AUTHOR]