Numerical analysis of a mathematical model of multiphase tissue growth

In this thesis we study a mathematical system of equations that models multi phase tissue growth. The mathematical system comprises of three coupled equations: an advection diffusion equation for a scalar quantity that defines the volume fraction of one cell type and two constitutive relations for the pressure field and volume averaged velocity field. A numerical discretisation of this mathematical model is derived using a coupled finite volume - finite difference scheme. Stability bounds on the approximate solution of a simplified version of the model are proved together with a convergence results relating the approximate solution to the weak solution of the simplified model. In addition an efficient and reliable numerical scheme is implemented in the Matlab programming language to solve the numerical approximation of the full model and computational results are presented.