Stabilized finite element schemes with LBB-stable elements for incompressible flows

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:177

Article

Gelhard, T ; Lube, G ; Olshanskii, MA ; Starcke, JH

关键词: finite element method;    stabilized method;    LBB condition;    Navier-Stokes equations;   

DOI  :  10.1016/j.cam.2004.09.017

来源: Elsevier

【 摘 要 】

We study stabilized FE approximations of SUPG type to the incompressible Navier-Stokes problem. Revisiting the analysis for the linearized model, we show that for conforming LBB-stable elements the design of the stabilization parameters for many practical flows differs from that commonly suggested in literature and initially designed for the case of equal-order approximation. Then we analyze a reduced SUPG scheme often used in practice for LBB-stable elements. To provide the reduced scheme with appropriate stability estimates we introduce a modified LBB condition which is proved for a family of FE approximations. The analysis is given for the linearized equations. Numerical experiments for some linear and nonlinear benchmark problems support the theoretical results. (C) 2004 Elsevier B.V. All rights reserved.

【 授权许可】

Free