Analysis of some mixed elements for the Stokes problem

✍ Scribed by Xiao-liang Cheng; Weimin Han; Hong-ci Huang

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 713 KB
• Volume: 85
• Category: Article
• ISSN: 0377-0427
• DOI: 10.1016/s0377-0427(97)00120-9

✦ Synopsis

In this paper we discuss some mixed finite element methods related to the reduced integration penalty method for solving the Stokes problem. We prove optimal order error estimates for bilinear-constant and biquadratic-bilinear velocity-pressure finite element solutions. The result for the biquadratic-bilinear element is new, while that for the bilinear-constant element improves the convergence analysis of Johnson and Pitk/iranta (1982). In the degenerate case when the penalty parameter is set to be zero, our results reduce to some related known results proved in by Brezzi and Fortin (1991) for the bilinearconstant element, and Bercovier and Pironneau (1979) for the biquadratic-bilinear element. Our theoretical results are consistent with the numerical results reported by Carey and Krishnan (1982) and Oden et al. (1982).