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A New L2 Projection Method for the Oseen Equations

Part of: Partial differential equations, boundary value problems

Published online by Cambridge University Press:  28 November 2017

Yanhong Bai  and
Minfu Feng
Yanhong Bai*
Affiliation:
College of Sciences, and Institute of Nonlinear Dynamics, Southwest Petroleum University, Chengdu, Sichuan 610500, China
Minfu Feng*
Affiliation:
School of Mathematics, Sichuan University, Chengdu, Sichuan 610064, China
*
*Corresponding author. Emails:baiyanhong1982@126.com (Y. H. Bai), fmf@wtjs.cn (M. F. Feng)
*Corresponding author. Emails:baiyanhong1982@126.com (Y. H. Bai), fmf@wtjs.cn (M. F. Feng)
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Abstract

In this paper, a new type of stabilized finite element method is discussed for Oseen equations based on the local L2 projection stabilized technique for the velocity field. Velocity and pressure are approximated by two kinds of mixed finite element spaces, Pl2–P1, (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.

Keywords

Oseen equationsL2 projection methodpressure projection method

MSC classification

Secondary: 65N12: Stability and convergence of numerical methods 65N30: Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 9 , Issue 6 , December 2017 , pp. 1420 - 1437
Copyright
Copyright © Global-Science Press 2017 

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