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 [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...
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| creator | Acosta-Soba, Daniel Guillén-González, Francisco Rodríguez Galván, J Rafael |
| description | 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. |
| doi_str_mv | 10.48550/arxiv.2304.09257 |
| format | Article |
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| subjects | Computer Science - Numerical Analysis Diffusion effects Mathematics - Numerical Analysis Tumors |
| title | A structure-preserving upwind DG scheme for a degenerate phase-field tumor model |
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