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.

翻译：我们认为,一种以衰落的抛物线系统为形式的肿瘤生长扩散界面模型的完全实用的有限要素近似值。 除了显示近似值的稳定性界限外,我们还证明我们趋于一致,从而在两个空间层面对这个系统存在解决办法。 几个数字实验证明了拟议方法的实用性和稳健性。