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

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 (P-1 - P-1 - P-1) and (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. (C) 2015 Elsevier B.V. All rights reserved.