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.
Cite this article
Joe Eyles, Robert Nürnberg, Vanessa Styles, Finite-element approximation of a phase field model for tumour growth. Port. Math. 78 (2021), no. 3/4, pp. 341–365DOI 10.4171/PM/2072