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An absolutely stabilized finite element method for the Stokes problem. (English) Zbl 0669.76051
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 Th. J. R. Hughes and L. P. Franca [Comput. Methods Appl. Mech. Eng. 65, 85-96 (1987; Zbl 0635.76067)]. Optimal error estimates in ${L}^{2}$-norm for the new stabilized finite element approximation of both the velocity and the pressure fields are established, as well as one in ${H}^{1}$-norm for the velocity field.

MSC:
 76D07 Stokes and related (Oseen, etc.) flows 65N30 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (BVP of PDE) 65N15 Error bounds (BVP of PDE)