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A posteriori error estimators for the Stokes equations. II: Non- conforming discretizations. (English) Zbl 0739.76035
Summary: [For part I, see: the author, ibid. 55, No. 3, 309-325 (1989; Zbl 0674.65092).]
We present an a posteriori error estimator for the nonconforming Crouzeix-Raviart discretization of the Stokes equations which is based on the local evaluation of residuals with respect to the strong form of the differential equation. The error estimator yields global upper and local lower bounds for the error of the finite element solution. It can easily be generalized to the stationary, incompressible Navier-Stokes equations and to other nonconforming finite element methods. Numerical examples show the efficiency of the proposed error estimator.

76M10 Finite element methods applied to problems in fluid mechanics
76D07 Stokes and related (Oseen, etc.) flows
76D05 Navier-Stokes equations for incompressible viscous fluids
65F10 Iterative numerical methods for linear systems
65N22 Numerical solution of discretized equations for boundary value problems involving PDEs
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