RESIDUAL-BASED A POSTERIORI ERROR ESTIMATES FOR A CONFORMING FINITE ELEMENT DISCRETIZATION OF THE STOKES-DARCY COUPLED PROBLEM

Abstract

We consider in this paper, a new a posteriori residual type error estimators for the Stokes-Darcy coupled problem analyzed in [1] on isotropic meshes. Our analysis covers two-and three-dimensional domains, conforming discretizations as well as different elements. 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, continuous inf-sup conditions satisfied by the bilinear forms involved, and local approximation properties. The a posteriori error estimate is based on a suitable evaluation on the residual of the finite element solution. It is proven that the a posteriori error estimate provided in this paper is both reliable and efficient.