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Analysis of mixed finite element methods for the Stokes problem: A unified approach. (English) Zbl 0535.76037
Summary: We develop a method for the analysis of mixed finite element methods for the Stokes problem in the velocity-pressure formulation. A technical ”macroelement condition” which is sufficient for the classical Babuška-Brezzi inequality [I. Babuška, Numer. Math. 20, 179-192 (1973; Zbl 0258.65108) and F. Brezzi, Revue Franc. Automat. Inform. Rech. Operat. 8, R-2, 129-151 (1974; Zbl 0338.90047)] to be valid, is introduced. Using this condition, we are able to verify the stability, and optimal order of convergence, of several known mixed finite element methods.

76D07 Stokes and related (Oseen, etc.) flows
76M99 Basic methods in fluid mechanics
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
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