Analysis of mixed finite element methods for the Stokes problem: A unified approach. (English) Zbl 0535.76037

Stenberg, Rolf

Math. Comput. 42, 9-23 (1984).

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.

MSC:

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

Keywords:

mixed finite element methods; velocity-pressure formulation; macroelement condition; Babuška-Brezzi inequality

Citations:

Zbl 0258.65108; Zbl 0338.90047