Journal of Pure and Applied Mathematics: Advances and ApplicationsAuthor's: Houedanou Koffi Wilfrid
Pages: [69] - [109]
Received Date: August 9, 2019
Submitted by:
DOI: http://dx.doi.org/10.18642/jpamaa_7100122087
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.
mixed finite elements, Stokes and Darcy equations, a posteriori error analysis.
