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A posteriori error estimates for the Stokes problem. (English) Zbl 0731.76040

A mixed finite element approximation of the Stokes problem is considered using a two-level iterative scheme applied to a mini-element discretization of the corresponding variational problem. An a posteriori error estimate is derived, based on the solution of a local Stokes problem in each element. This estimate is compared with an estimate derived from the Petrov-Galerkin approximation and is shown to be both a global upper and lower bound of the discretization error. This estimate is tested on the following problems: a driven cavity in a unit square; backward facing step; disk with a crack.
Reviewer: P.K.Kythe

MSC:

76M10 Finite element methods applied to problems in fluid mechanics
76D07 Stokes and related (Oseen, etc.) flows
65N15 Error bounds for boundary value problems involving PDEs
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