On numerical approximations to diffuse-interface tumor growth models

Abstract

This work is devoted to developing new numerical schemes for a tumor-nutrient PDE model. It is based on phase field equations for the tumor variable and a diffusive equation for the nutrient one, coupled by reaction terms and cross-diffusion terms. The model conserves the sum of tumor+nutrient and has a dissipative energy law. We introduce two different time-discrete schemes: one is based on an Eyre-type decomposition of the energy and the other is an energy quadratization scheme. Both (continuous) Finite Elements and Discontinuous Galerkin are used for space discretization. The schemes are compared analytically and computationally.