The study of polymer flooding is of utmost relevance due to the diversity of applications. This thesis presents an innovative mathematical and computational model for polymer flooding at porous media that effectively integrates the process in the near-well region and the reservoir. In the mathematical model, along with the single-phase flow and transport equations, we propose closure relationships for the adsorption isotherms, mechanical retention kinetics, and non-Newtonian pseudoplastic behavior. For the computational model, we employ the Dirichlet-Neumann Domain Decomposition method. The resulting system of equations is discretized using the finite element method and linearized through the Newton-Raphson method. Subsequently, we verify the accuracy of the proposed method by comparing the discrete solutions with analytical and high-fidelity solutions. We also explore the effects of non-Newtonian behavior, mechanical retention, and formation damage on polymer transport in a 2D domain replicating a five-spot injection pattern. The numerical simulations demonstrate that the proposed computational model effectively captures solutions for polymer injection in porous media across various scenarios.