Numerical analysis for a Cahn–Hilliard system modelling tumour growth with chemotaxis and active transport

Abstract A diffuse interface model for tumour growth in the presence of a nutrient consumed by is considered. The system equations consists Cahn–Hilliard equation with source terms cells and reaction–diffusion nutrient. We introduce fully-discrete finite element approximation prove stability bounds discrete scheme. Moreover, we show that solutions exist depend continuously on initial boundary data. then pass to limit discretization parameters convergence global-in-time weak solution model. Under additional assumptions, this unique. Finally, present some numerical results including error investigation one spatial dimension long time simulations two three dimensions.