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Error estimates for a mixed finite element approximation of the Stokes equations. (English) Zbl 0557.76037
The author considers a mixed finite element method for the Stokes problem in a polygonal domain $$\Omega \subset {\mathbb{R}}^ 2$$. He establishes a discrete inf-sup condition, which fits into the abstract error analysis of F. Brezzi [ibid. 8, 129-151 (1974; Zbl 0338.90047)] for mixed problems. Using linear finite elements, $$O(h^{\alpha})$$-error estimates for the energy norm of the velocity and the $$L^ 2$$-norm of the pressure are derived. If the domain $$\Omega$$ is convex, the exponent equals 1, otherwise it only depends on the greatest interior angle at a corner of $$\Omega$$. When using piecewise quadratic functions for the velocity he gets improved error estimates provided $$f\in H^ 1(\Omega)$$ and $$\Omega$$ is convex.
Reviewer: J.Groß

##### 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
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##### References:
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