We introduce and analyze a discontinuous Galerkin method for the numerical modelling of the equations of Multiple-Network Poroelastic Theory (MPET) in the dynamic formulation. The MPET model can comprehensively describe functional changes in the brain considering multiple scales of fluids. Concerning the spatial discretization, we employ a high-order discontinuous Galerkin method on polygonal and polyhedral grids and we derive stability and a priori error estimates. The temporal discretization is based on a coupling between a Newmark $\beta$-method for the momentum equation and a $\theta$-method for the pressure equations. After the presentation of some verification numerical tests, we perform a convergence analysis using an agglomerated mesh of a geometry of a brain slice. Finally we present a simulation in a three dimensional patient-specific brain reconstructed from magnetic resonance images. The model presented in this paper can be regarded as a preliminary attempt to model the perfusion in the brain.

翻译：我们引入并分析了一种不连续Galerkin方法，用于动态模式下的多网络孔弹理论（MPET）方程的数值模拟。MPET模型可以全面描述考虑多种尺度的流体的脑功能变化。就空间离散而言，我们在多边形和多面体网格上采用高阶不连续Galerkin方法，并导出稳定性和先验误差估计。时间离散基于动量方程的Newmark β方法和压力方程的θ方法之间的耦合。在介绍一些验证数值测试后，我们使用脑切片的一个聚合网格进行收敛分析。最后，我们在磁共振图像重建的三维患者特定脑部进行了模拟。本文介绍的模型可以被视为对脑灌注进行建模的初步尝试。