The modeling of brain fluid flow and solute transport involves the coupling of cerebrospinal fluid sCSF) flow with the poromechanics of the cerebral tissue and the pulsatile blood perfusion in the brain. Accurately simulating these interactions is crucial for understanding physiological and pathological processes, such as waste clearance mechanisms implicated in neurodegenerative diseases. In this talk, we introduce a computational framework that couples the Stokes equations, modeling CSF flow, with Multiple-network Poroelasticity (MPE) equations, representing the deformation and fluid transport within brain tissue. The spatial discretization employs a high-order Polytopal Discontinuous Galerkin (PolyDG) method, naturally suitable for handling complex geometries typical of brain structures. To ensure the reliability and efficiency of our simulations, we discuss both a priori and a posteriori error estimation results. In particular, a posteriori estimates provide a foundation for adaptive mesh refinement strategies, aiming at an efficient use of computational resources while maintaining solution accuracy. Through numerical experiments, we demonstrate the effectiveness of our adaptive approach in capturing critical features of brain fluid dynamics. Moreover, we quantitatively assess the advantages of the PolyDG method in dealing with fine-detailed geometries. The results underscore the potential of integrating advanced numerical methods with rigorous error estimation to enhance the fidelity and efficiency of simulations in complex multiphysics scenarios. Acknowledgments. IF and NP have been partially supported by ICSC-Centro Nazionale di Ricerca in High Performance Computing, Big Data, e Quantum Computing funded by the European Union-NextGenerationEU plan. PA and MV have been partially funded by the European Union (ERC SyG, NEMESIS, project number 101115663). All authors are members of GNCS-INdAM, and IF acknowledges the support of the GNCS-INdAM project CUP E53C23001670001. This work is part of the activities of “Dipartimento di Eccellenza 2023-2027”.