(untitled) (Advances in Applied Mathematics and Mechanics, 2021)
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.