TY - JOUR
T1 - Improved Local Projection for the Generalized Stokes Problem
AU - Nafa , Kamel
JO - Advances in Applied Mathematics and Mechanics
VL - 6
SP - 862
EP - 873
PY - 2009
DA - 2009/01
SN - 1
DO - http://doi.org/10.4208/aamm.09-m09S07
UR - https://global-sci.org/intro/article_detail/aamm/8402.html
KW - Generalized Stokes equations, stabilized finite elements, local projection, convergence, error estimates.
AB - <p style="text-align: justify;">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.</p>