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Finite-element approximation of a phase field model for tumour growth. (English) Zbl 07478508

Summary: We consider a fully practical finite-element approximation of a diffuse interface model for tumour growth that takes the form of a degenerate parabolic system. In addition to showing stability bounds for the approximation, we prove convergence, and hence existence of a solution to this system in two space dimensions. Several numerical experiments demonstrate the practicality and robustness of the proposed method.

MSC:

65-XX Numerical analysis
35K45 Initial value problems for second-order parabolic systems
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
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