TY - JOUR
T1 - Equal order approximations enriched with bubbles for coupled Stokes-Darcy problem
AU - Nafa, Kamel
PY - 2014/11
Y1 - 2014/11
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
AN - SCOPUS:84901199885
SN - 0377-0427
VL - 270
SP - 275
EP - 282
JO - Journal of Computational and Applied Mathematics
JF - Journal of Computational and Applied Mathematics
ER -