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Superconvergence of nonconforming finite element method for the Stokes equations. (English) Zbl 1003.65121
The numerical solution of the Stokes problem with the aid of the nonconforming finite element method is considered. The superconvergence is obtained using a least-squares surface fitting method proposed by J. Wang for the standard Galerkin method [J. Math. Study 33, No. 3, 229-243 (2000; Zbl 0987.65108)]. The regularly of the solution is assumed. The obtained results are applicable for any pairs of nonconforming stable finite elements. Two examples of elements (Crousier-Raviart and Douglas quadrilateral) are presented.

MSC:
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
76D07 Stokes and related (Oseen, etc.) flows
76M10 Finite element methods applied to problems in fluid mechanics
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35J25 Boundary value problems for second-order elliptic equations
35Q30 Navier-Stokes equations
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