In this paper we present and analyze a fully-mixed formulation for the coupled problem arising in the interaction between a free fluid and a flow in a poroelastic medium. The flows are governed by the Stokes and Biot equations, respectively, and the transmission conditions are given by mass conservation, balance of stresses, and the Beavers-Joseph-Saffman law. We apply dual-mixed formulations in both domains, where the symmetry of the Stokes and poroelastic stress tensors is imposed by setting the vorticity and structure rotation tensors as auxiliary unknowns. In turn, since the transmission conditions become essential, they are imposed weakly, which is done by introducing the traces of the fluid velocity, structure velocity, and the poroelastic media pressure on the interface as the associated Lagrange multipliers. The existence and uniqueness of a solution are established for the continuous weak formulation, as well as a semidiscrete continuous-in-time formulation with non-matching grids, together with the corresponding stability bounds. In addition, we develop a new multipoint stress-flux mixed finite element method by involving the vertex quadrature rule, which allows for local elimination of the stresses, rotations, and Darcy fluxes. Well-posedness and error analysis with corresponding rates of convergences for the fully-discrete scheme are complemented by several numerical experiments.

翻译：在本文中,我们提出并分析一个完全混合的配方,以解决在自由流体和孔状介质流动之间相互作用产生的问题。流体分别由斯托克斯和比奥特方程式管理,传输条件则由质量保护、压力平衡和比弗斯-约瑟夫-萨夫曼法提供。我们在这两个领域都采用了双重混合的配方,将静态和孔状压力压强的对称性与不匹配的电网的半分位连续时间配方加上相应的稳定性界限。此外,由于传输条件变得至关重要,因此流动流动受软性制约,这是通过引入流动速度、结构速度的痕迹和对界面作为相关拉格朗乘数的孔状介质压力。为持续弱化的配方和不匹配的电网的半分位连续配方,以及相应的稳定性界限。此外,我们通过引入新的多点压力率、结构速度和对接轨率的递增率分析,从而允许通过数位阶调整调和平流体压力的平流率进行新的多点递升回式组合。