Equal order approximations enriched with bubbles for coupled Stokes-Darcy problem

Kamel Nafa*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)


As a remedy to the instability of the Galerkin finite element formulation, symmetric stabilization techniques such as the continuous interior penalty, the subgrid and local projection methods were proposed and analyzed by Burman and Hansbo (2006) [10], Badia and Codina (2009) [11], Becker and Braack (2001) [12], and Nafa and Wathen (2009) [13]. 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 finite elements in the two parts, such as Taylor-Hood or MINI elements for the Stokes domain, and mixed elements of Raviart-Thomas elements type for the Darcy domain. Here, we discretize by standard equal-order finite elements enriched with bubbles functions and use local projection stabilization technique (LPS) to stabilize the method and control the fluctuation of the velocity divergence vector on the Darcy region. We also suggest a way to control the natural H(div) velocity.

Original languageEnglish
Pages (from-to)275-282
Number of pages8
JournalJournal of Computational and Applied Mathematics
Publication statusPublished - Nov 2014


  • Darcy equation
  • Flows in porous media
  • Mixed elements
  • Stabilized finite elements
  • Stokes equations

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics


Dive into the research topics of 'Equal order approximations enriched with bubbles for coupled Stokes-Darcy problem'. Together they form a unique fingerprint.

Cite this