Glioblastoma Multiforme is a brain cancer that still show poor prognosis for patients despite the active researches for new treatments. In this work the goal is to model and simulate the evolution of tumour associated angiogenesis and the therapeutic response of the Glioblastoma Multiforme. Multiple phenomena are modelled in order to fit different biological pathways, such as, the cellular cycle, apoptosis, hypoxia or angiogenesis.This results in a nonlinear system with 4 equations and 4 unknowns: the density of tumour cells, the $O_{2}$ concentration, the density of endothelial cells and the vascular endothelial growth factor concentration.This system is solved numerically on a 2D-slice of Magnetic Resonance Imaging, using a nonlinear control volume finite element scheme on a mesh fitting the geometry of the brain and the tumour of a patient.We show that this implicit volume finite element numerical scheme is positive and we give energy estimates on the discrete solution to ensure convergence.The numerical scheme is implicit in time.Numerical simulations of this scheme have been done using the different standard treatments: surgery, chemotherapy and radiotherapy, in order to understand the behaviour of tumour in response to treatments.