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Zbl 0669.76051
Douglas, Jim jun.; Wang, Junping
An absolutely stabilized finite element method for the Stokes problem. (English)
[J] Math. Comput. 52, No.186, 495-508 (1989). ISSN 0025-5718; ISSN 1088-6842/e

An absolutely stabilized finite element formulation for the Stokes problem is presented in this paper. This new formulation, which is nonsymmetric but stable without employing of any stability constant, can be regarded as a modification of the formulation porposed recently by {\it Th. J. R. Hughes} and {\it L. P. Franca} [Comput. Methods Appl. Mech. Eng. 65, 85-96 (1987; Zbl 0635.76067)]. Optimal error estimates in $L\sp 2$-norm for the new stabilized finite element approximation of both the velocity and the pressure fields are established, as well as one in $H\sp 1$-norm for the velocity field.

MSC 2000:: *76D07 Stokes flows
65N30 Finite numerical methods (BVP of PDE)
65N15 Error bounds (BVP of PDE)

Keywords: absolutely stabilized finite element formulation; Stokes problem

Citations: Zbl 0635.76067

Cited in: Zbl 1240.76017 Zbl 0943.76048 Zbl 0759.76040

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