论文标题
stokes-biot模型的多点应力 - 频率混合有限元法
A multipoint stress-flux mixed finite element method for the Stokes-Biot model
论文作者
论文摘要
在本文中，我们介绍并分析了一个完全混合的公式，用于在毛弹性培养基中自由流体与流动之间的相互作用中产生的耦合问题。流量分别受Stokes和Biot方程的约束，并且传播条件由质量保护，压力平衡和海狸 - 约瑟夫·塞夫曼法律给出。我们在两个结构域中应用双重混合配方，其中通过将涡度和结构旋转张量定为辅助未知数来施加Stokes和Poro弹性应力张量的对称性。反过来，由于传输条件变得必不可少，因此它们被弱施加，这是通过引入流体速度，结构速度和界面上的毛弹性介质压力作为相关的Lagrange乘数来完成的。为连续的弱公式以及具有非匹配网格的半分化连续公式建立了解决方案的存在和唯一性，以及相应的稳定性界限。此外，我们通过涉及顶点正交规则来开发一种新的多点应力混合有限元方法，该方法允许局部消除应力，旋转和Darcy通量。适当的和误差分析，以及完全消失方案的相应收敛速率，由几个数值实验补充。
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.
