Finite element approximation of a phase field model for tumour growth

TL;DR

This paper develops and analyzes a finite element method for a diffuse interface model of tumour growth, proving stability, convergence, and demonstrating robustness through numerical experiments in two dimensions.

Contribution

It introduces a practical finite element approximation for a degenerate parabolic tumour growth model, with proven stability and convergence results.

Findings

The method is stable and convergent in two dimensions.

Numerical experiments confirm robustness and practicality.

The approach effectively handles the degenerate parabolic system.

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.