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Superconvergence of discontinuous Galerkin finite element method for the stationary Navier‐Stokes equations
Author(s) -
Li Jian,
He Yinnian
Publication year - 2007
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.20188
Subject(s) - superconvergence , mathematics , finite element method , discontinuous galerkin method , mathematical analysis , navier–stokes equations , extended finite element method , mixed finite element method , solenoidal vector field , galerkin method , pressure correction method , partial differential equation , hp fem , smoothed finite element method , compressibility , vector field , finite element limit analysis , boundary knot method , geometry , physics , mechanics , boundary element method , thermodynamics
This article focuses on discontinuous Galerkin method for the 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 the standard conforming finite element. Then, superconvergence of nonconforming finite element approximations is applied by using least‐squares surface fitting for the stationary Navier‐Stokes equations. The method ameliorates the two noticeable disadvantages about the given finite element pair. Finally, the superconvergence result is provided under some regular assumptions. © 2006 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 23: 421–436, 2007