The discretization of fluid-poromechanics systems is typically highly demanding in terms of computational effort. This is particularly true for models of multiphysics flows in the brain, due to the geometrical complexity of the cerebral anatomy - requiring a very fine computational mesh for finite element discretization - and to the high number of variables involved. Indeed, this kind of problems can be modeled by a coupled system encompassing the Stokes equations for the cerebrospinal fluid in the brain ventricles and Multiple-network Poro-Elasticity (MPE) equations describing the brain tissue, the interstitial fluid, and the blood vascular networks at different space scales. The present work aims to rigorously derive a posteriori error estimates for the coupled Stokes-MPE problem, as a first step towards the design of adaptive refinement strategies or reduced order models to decrease the computational demand of the problem. Through numerical experiments, we verify the reliability and optimal efficiency of the proposed a posteriori estimator and identify the role of the different solution variables in its composition.

翻译：流体-多孔介质力学系统的离散化通常在计算量方面要求极高。对于大脑中的多物理场流动模型而言尤其如此，这既源于大脑解剖结构的几何复杂性——需要非常精细的计算网格进行有限元离散，也源于所涉及变量的数量众多。事实上，此类问题可以通过一个耦合系统进行建模，该系统包含描述脑室中脑脊液的Stokes方程，以及描述脑组织、间质液和不同空间尺度下血管网络的多网络多孔弹性（MPE）方程。本研究旨在严格推导耦合Stokes-MPE问题的后验误差估计，作为设计自适应细化策略或降阶模型以降低问题计算需求的第一步。通过数值实验，我们验证了所提出的后验误差估计器的可靠性和最优效率，并识别了不同解变量在其构成中的作用。