Table of Contents
Advances in Numerical Analysis
Volume 2016, Article ID 7389102, 9 pages
http://dx.doi.org/10.1155/2016/7389102
Research Article

Analysis of Subgrid Stabilization Method for Stokes-Darcy Problems

Department of Mathematics and Statistics, Sultan Qaboos University, College of Science, P.O. Box 36, Al-Khoudh 123, Muscat, Oman

Received 27 April 2016; Revised 31 July 2016; Accepted 16 August 2016

Academic Editor: Weimin Han

Copyright © 2016 Kamel Nafa. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

A number of techniques, used as remedy to the instability of the Galerkin finite element formulation for Stokes like problems, are found in the literature. In this work we consider a coupled Stokes-Darcy problem, where in one part of the domain the fluid motion is described by Stokes equations and for the other part the fluid is in a porous medium and described by Darcy law and the conservation of mass. Such systems can be discretized by heterogeneous mixed finite elements in the two parts. A better method, from a computational point of view, consists in using a unified approach on both subdomains. Here, the coupled Stokes-Darcy problem is analyzed using equal-order velocity and pressure approximation combined with subgrid stabilization. We prove that the obtained finite element solution is stable and converges to the classical solution with optimal rates for both velocity and pressure.