TY - JOUR
T1 - Improved local projection for the generalized stokes problem
AU - Nafa, Kamel
PY - 2009
Y1 - 2009
N2 - We analyze pressure stabilized finite element methods for the solution of the generalized Stokes problem and investigate their stability and convergence properties. An important feature of the methods is that the pressure gradient unknowns can be eliminated locally thus leading to a decoupled system of equations. Although the stability of the method has been established, for the homogeneous Stokes equations, the proof given here is based on the existence of a special interpolant with additional orthogonal property with respect to the projection space. This makes it much simpler and more attractive. The resulting stabilized method is shown to lead to optimal rates of convergence for both velocity and pressure approximations.
AB - We analyze pressure stabilized finite element methods for the solution of the generalized Stokes problem and investigate their stability and convergence properties. An important feature of the methods is that the pressure gradient unknowns can be eliminated locally thus leading to a decoupled system of equations. Although the stability of the method has been established, for the homogeneous Stokes equations, the proof given here is based on the existence of a special interpolant with additional orthogonal property with respect to the projection space. This makes it much simpler and more attractive. The resulting stabilized method is shown to lead to optimal rates of convergence for both velocity and pressure approximations.
KW - Convergence
KW - Error estimates
KW - Generalized stokes equations
KW - Local projection
KW - Stabilized finite elements
UR - http://www.scopus.com/inward/record.url?scp=84863498739&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84863498739&partnerID=8YFLogxK
U2 - 10.4208/aamm.09-m09S07
DO - 10.4208/aamm.09-m09S07
M3 - Article
AN - SCOPUS:84863498739
SN - 2070-0733
VL - 1
SP - 862
EP - 873
JO - Advances in Applied Mathematics and Mechanics
JF - Advances in Applied Mathematics and Mechanics
IS - 6
ER -