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Superconvergence of finite element approximations for the Stokes problem by projection methods. (English) Zbl 1002.65118
This paper deals with a general superconvergence result for finite element approximations of the Stokes problem by using the \(L^2\)-projection for the standard Galerkin method. The superconvergence result is based on some regularity assumptions for the Stokes problem and is applicable to any finite element method (FEM) with regular but nonuniform partitions. The authors apply the general superconvergence result to three particular FEMs and improve the existing error estimate by using the \(L^2\)-projection method.

MSC:
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
65N15 Error bounds for boundary value problems involving PDEs
35Q30 Navier-Stokes equations
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
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