A New $L^2$ Projection Method for the Oseen Equations (Advances in Applied Mathematics and Mechanics, 2021)
In this paper, a new type of stabilized finite element method is discussed forOseen equations based on the local $L^2$ projection stabilized technique for the velocityfield. Velocity and pressure are approximated by two kinds of mixed finite elementspaces, $P^2_l$−$P_1$, ($l$ = 1,2). A main advantage of the proposed method lies in that, allthe computations are performed at the same element level, without the need of nestedmeshes or the projection of the gradient of velocity onto a coarse level. Stability andconvergence are proved for two kinds of stabilized schemes. Numerical experimentsconfirm the theoretical results.