To cure the illness in the brain glioblastoma, the Gliadel wafer, as the first FDA-approved chemotherapy, was available on the market since 1997. Due to the complex studies in vivo, more and more researchers have paid their attention to investigate the dynamic process in the brain by numerical methods. This study aimed to simulate the drug concentration in the cavity after drug releases from Gliadel wafers into the brain tumor by a two-dimensional simulation. The government equations, the parameters, and corresponding initial and boundary conditions are specified. Then the models are discretized and solved by finite element method (FEM) and finite difference method (FDM) based on C++ library Adaptive Finite Element Package (AFEPack) and MATLAB, respectively. First of all, the numerical convergence of the method is studied by numerical results represented in several successively refined meshes, which shows the reliability of our method. In the results from FEM, a steady state of the pressure in the normal tissue can be simulated. As for FDM, the changes of drug concentration are displayed at six different times. The numerical method in this paper is an effective tool for the numerical study on drug release from polymers. Additionally, convection is a critical factor in drug transportation. Moreover, the simulation approach can be used as the guild for remedy optimization and dynamic analysis of other drugs (paclitaxel) for tumor treatment in the clinic. This mathematical model has wide applications about drug release in multiple dosage forms, such as long sustained release microspheres, oral extended release hydrophilic matrix tablets, hydrogel, and sustained release topical rings.