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Superconvergence of discontinuous Galerkin finite element method for the stationary Navier‐Stokes equations
Authors:Jian Li  Yinnian He
Affiliation:1. Faculty of Science, Xi'an Jiaotong University, Xi'an,710049, PR China;2. Department of Mathematics, Baoji University of Arts and Sciences, Baoji, 721007, PR China;3. Faculty of Science, Xi'an Jiaotong University, Xi'an,710049, PR ChinaFaculty of Science, Xi'an Jiaotong University, Xi'an,710049, PR China
Abstract: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
Keywords:Navier‐Stokes equations  nonconforming finite element  conforming finite element  Inf‐sup condition  least‐squares surface fitting
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