JournalspmVol. 78, No. 3/4pp. 341–365

Finite-element approximation of a phase field model for tumour growth

  • Joe Eyles

    University of Sussex, Brighton, UK
  • Robert Nürnberg

    University of Trento, Italy
  • Vanessa Styles

    University of Sussex, Brighton, UK
Finite-element approximation of a phase field model for tumour growth cover
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Abstract

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. 341–365

DOI 10.4171/PM/2072