Numerical analysis of a mathematical model describing the evolution of hypoxic glioma cells.

In this work, we develop the numerical analysis of a parabolic system of PDE describing the proliferation-invasion structure of hypoxic glial cells in the brain. Explicitly, we propose a fully discrete numerical scheme, based on a semi-implicit Euler discretization in time and Finite Element (FE) discretization on space, for approximating the solutions of the continuous model. For this numerical scheme we prove some properties including well-posedness, positivity, maximum principle, uniform estimates, convergence towards weak solutions, optimal error estimates and asymptotic behaviour of the discrete solutions. Finally, we present some numerical simulations which validate the theoretical results. [ABSTRACT FROM AUTHOR]