Volume 9, Issue 6
A New $L^2$ Projection Method for the Oseen Equations

Adv. Appl. Math. Mech., 9 (2017), pp. 1420-1437.

Published online: 2017-09

Cited by

Export citation
• Abstract

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.

65N12, 65N30

• BibTex
• RIS
• TXT
@Article{AAMM-9-1420, author = {Bai , Yanhong and Feng , Minfu}, title = {A New $L^2$ Projection Method for the Oseen Equations}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2017}, volume = {9}, number = {6}, pages = {1420--1437}, abstract = {

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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.2016.m1420}, url = {http://global-sci.org/intro/article_detail/aamm/10186.html} }
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 -

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.

Yanhong Bai & Minfu Feng. (2020). A New $L^2$ Projection Method for the Oseen Equations. Advances in Applied Mathematics and Mechanics. 9 (6). 1420-1437. doi:10.4208/aamm.2016.m1420
Copy to clipboard
The citation has been copied to your clipboard