A mortar method using nonconforming and mixed finite elements for the coupled Stokes-Darcy model
A mortar method using nonconforming and mixed finite elements for the coupled Stokes-Darcy model
复制标题
耦合Stokes-Darcy模型中非相容混合有限元的砂浆法
DOI：
10.4208/aamm.2016.m1397
复制
发表时间：
2017
影响因子：
1.4
通讯作者：
Mingchao Cai
中科院分区：
文献类型：
--
作者：
Peiqi Huang;Jinru Chen;Mingchao Cai
本文研究了流体-多孔介质耦合渗流模型的数值方法。该模型由两个相邻子域的Stokes方程和Darcy方程组成，通过一定的界面条件耦合在一起。耦合模型的弱形式为鞍点型。提出了一种砂浆有限元方法来近似耦合问题的弱形式。在该方法中，流体子区域采用C-Crouzeix-Raviart单元，多孔介质子区域采用最低阶Raviart-Thomas单元;不同子区域的网格在公共界面上可以不匹配;通过在有限元空间的定义中加入约束，弱地施加界面条件。离散问题的适定性和所提出的方法的最佳误差估计。数值实验也证实了理论结果。
In this work, we study numerical methods for a coupled fluid-porous media flow model. The model consists of Stokes equations and Darcy's equations in two neighboring subdomains, coupling together through certain interface conditions. The weak form for the coupled model is of saddle point type. A mortar finite element method is proposed to approximate the weak form of the coupled problem. In our method, nonconforming Crouzeix-Raviart elements are applied in the fluid subdomain and the lowest order Raviart-Thomas elements are applied in the porous media subdomain; Meshes in different subdomains are allowed to be nonmatching on the common interface; Interface conditions are weakly imposed via adding constraint in the definition of the finite element space. The well-posedness of the discrete problem and the optimal error estimate for the proposed method are established. Numerical experiments are also given to confirm the theoretical results.