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Superconvergence of discontinuous Galerkin finite element method for the stationary Navier-Stokes equations. (English) Zbl 1107.76046
Summary: This article focuses on discontinuous Galerkin method for two- or three-dimensional stationary incompressible Navier-Stokes equations. The velocity field is approximated by discontinuous locally solenoidal finite element, and the pressure is approximated by standard conforming finite element. Then, superconvergence of nonconforming finite element approximations is applied by using least-squares surface fitting for stationary Navier-Stokes equations. The method ameliorates two noticeable disadvantages of the given finite element pair. The superconvergence result is provided under some regularity assumptions.

MSC:
76M10 Finite element methods applied to problems in fluid mechanics
76D05 Navier-Stokes equations for incompressible viscous fluids
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
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