A Residual-Based A Posteriori Error Estimator for the Stokes-Darcy Coupled Problem

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 residualbased 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 Cl

• Type: Journal
• Year: 2010
• Where: SIAMNUM
• Authors: Ivo Babuska, Gabriel N. Gatica
• Keywords: Finite Element, Posteriori Error, Posteriori Error Analysis, SIAMNUM 2010