A RESIDUAL-BASED A POSTERIORI ERROR ESTIMATOR FOR THE STOKES-DARCY COUPLED PROBLEM

被引:73
作者
Babuska, Ivo [1 ]
Gatica, Gabriel N. [2 ,3 ]
机构
[1] Univ Texas Austin, Inst Computat Engn & Sci, Austin, TX 78712 USA
[2] Univ Concepcion, CIMA2, Concepcion, Chile
[3] Univ Concepcion, Dept Ingn Matemat, Concepcion, Chile
关键词
a posteriori error analysis; Stokes equation; Darcy equation; FINITE-ELEMENT-METHOD; POROUS-MEDIA; FLUID-FLOW; EQUATIONS;
D O I
10.1137/080727646
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
In this paper we develop an a posteriori error analysis of a new conforming mixed finite element method for the coupling of fluid flow with porous media flow. The flows are governed by the Stokes and Darcy equations, respectively, and the transmission conditions are given by mass conservation, balance of normal forces, and the Beavers-Joseph-Saffman law. The finite element subspaces consider Bernardi-Raugel and Raviart-Thomas elements for the velocities, piecewise constants for the pressures, and continuous piecewise linear elements for a Lagrange multiplier defined on the interface. We derive a reliable and efficient residual-based a posteriori error estimator for this coupled problem. The proof of reliability makes use of suitable auxiliary problems, diverse continuous inf-sup conditions satisfied by the bilinear forms involved, and local approximation properties of the Clement interpolant and Raviart-Thomas operator. On the other hand, Helmholtz decomposition, inverse inequalities, and the localization technique based on triangle-bubble and edge-bubble functions are the main tools for proving the efficiency of the estimator. Up to minor modi. cations, our analysis can be extended to other finite element subspaces yielding a stable Galerkin scheme.
引用
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页码:498 / 523
页数:26
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