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A local superconvergence analysis of the finite element method for the Stokes equations by local projections. (English) Zbl 1227.65115
Summary: We focus on a local superconvergence analysis of the finite element method for the Stokes equations by local projections. The local and global superconvergence results of finite element solutions are provided for the Stokes problem under some corresponding regularity assumptions. Conclusion can be drawn that the local superconvergence has advantages over the global superconvergence in two important aspects. On the one hand, it offsets theoretical limitation in practical applications. On the other hand, interior estimates are derived on the base of local properties of the domain without global smoothness for the exact solution and prior regularity of the problem globally over the whole domain.

MSC:
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35Q35 PDEs in connection with fluid mechanics
76D05 Navier-Stokes equations for incompressible viscous fluids
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