TY - JOUR
T1 - A New $L^2$ Projection Method for the Oseen Equations
AU - Bai , Yanhong
AU - Feng , Minfu
JO - Advances in Applied Mathematics and Mechanics
VL - 6
SP - 1420
EP - 1437
PY - 2017
DA - 2017/09
SN - 9
DO - http://doi.org/10.4208/aamm.2016.m1420
UR - https://global-sci.org/intro/article_detail/aamm/10186.html
KW - Oseen equations, $L^2$ projection method, pressure projection method.
AB - <p style="text-align: justify;">In this paper, a new type of stabilized finite element method is discussed for
Oseen equations based on the local $L^2$ projection stabilized technique for the velocity
field. Velocity and pressure are approximated by two kinds of mixed finite element
spaces, $P^2_l$−$P_1$, ($l$ = 1,2). A main advantage of the proposed method lies in that, all
the computations are performed at the same element level, without the need of nested
meshes or the projection of the gradient of velocity onto a coarse level. Stability and
convergence are proved for two kinds of stabilized schemes. Numerical experiments
confirm the theoretical results.</p>