### Abstract

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 language | English |
---|---|

Pages (from-to) | 275-282 |

Number of pages | 8 |

Journal | Journal of Computational and Applied Mathematics |

Volume | 270 |

DOIs | |

Publication status | Published - 2014 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Computational Mathematics
- Applied Mathematics

### Cite this

**Equal order approximations enriched with bubbles for coupled Stokes-Darcy problem.** / Nafa, Kamel.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Equal order approximations enriched with bubbles for coupled Stokes-Darcy problem

AU - Nafa, Kamel

PY - 2014

Y1 - 2014

N2 - 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.

AB - 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.

KW - Darcy equation

KW - Flows in porous media

KW - Mixed elements

KW - Stabilized finite elements

KW - Stokes equations

UR - http://www.scopus.com/inward/record.url?scp=84901199885&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84901199885&partnerID=8YFLogxK

U2 - 10.1016/j.cam.2014.01.010

DO - 10.1016/j.cam.2014.01.010

M3 - Article

VL - 270

SP - 275

EP - 282

JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

SN - 0377-0427

ER -