DARCT-STOKES耦合问题的H（div）有限元逼近方法

H(div) conforming finite element methods for the coupled Darcy-Stokes problem

摘要:

文章主要研究了darcy-Stokes耦合流动问题的数值解.darcy-Stokes的耦合模型由流体域的stokes方程，多孔介质域的darcy方程及两区域的界面的界面条件所构成. 通过在界面引入lagrange乘数，将耦合的darcy-Stokes的模型转化为了鞍点问题进行处理，同时利用了H(div)协调的T-R元对该耦合问题进行了离散，证明了离散 问题解的存在唯一性，且进行了误差估计.

Abstract:

The numerical solution of coupled Darcy-Stokes flow problem is studied in this paper. The coupled Darcy-Stokes flow models are composed by Stokes equation in the flow domain and by Darcy's law in porous medium domain, and by proper interface conditions between the two domains. By introduced Lagrange multipliers to process interface, New variational form for coupled Darcy-Stokes model is proposed. The problem is discreted by the low order conforming H(div) R-T elements . Lastly, we prove the existence and uniqueness of the discrete problem and get error estimates.