A stabilized finite element method based on two local Gauss integrations for a coupled Stokes-Darcy problem

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• 作者：Rui Li^a ; ^{liruixjtu@163.com" class="auth_mail" title="E-mail the corresponding author} ; Jian Li^b ; ^c ; ^{jiaaanli@gmail.com" class="auth_mail" title="E-mail the corresponding author} ; Zhangxin Chen^a ; ^d ; ^e ; ^{zhachen@ucalgary.ca" class="auth_mail" title="E-mail the corresponding author} ; Yali Gao^a ; ^{gaoyli2008@163.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Coupled Stokes&ndash ; Darcy flow ; Stability ; Lowest equal-order elements ; Beavers&ndash ; Joseph&ndash ; Saffman&ndash ; Jones ; Beavers&ndash ; Joseph ; Gauss integration
• 刊名：Journal of Computational and Applied Mathematics
• 出版年：2016
• 出版时间：15 January 2016
• 年：2016
• 卷：292
• 期：Complete
• 页码：92-104
• 全文大小：870 K

文摘

In this paper, a stabilized mixed finite element method for a coupled steady Stokes–Darcy problem is proposed and investigated. This method is based on two local Gauss integrals for the Stokes equations. Its originality is to use a difference between a consistent mass matrix and an under-integrated mass matrix for the pressure variable of the coupled Stokes–Darcy problem by using the lowest equal-order finite element triples. This new method has several attractive computational features: parameter free, flexible, and altering the difficulties inherited in the original equations. Stability and error estimates of optimal order are obtained by using the lowest equal-order finite element triples (P₁−P₁−P₁)$(P_1-P_1-P_1)$ and (Q₁−Q₁−Q₁)$(Q_1-Q_1-Q_1)$ for approximations of the velocity, pressure, and hydraulic head. Finally, a series of numerical experiments are given to show that this method has good stability and accuracy for the coupled problem with the Beavers–Joseph–Saffman–Jones and Beavers–Joseph interface conditions.