Superconvergence analysis for the Navier---Stokes equations

Authors:
Xiaoshen Wang;Xiu Ye
Affiliations:
Department of Mathematics, University of Arkansas at Little Rock, Little Rock, AR;Department of Mathematics, University of Arkansas at Little Rock, Little Rock, AR
Venue:
Applied Numerical Mathematics
Year:
2002

Citing 5
Cited 1

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SIAM Journal on Numerical Analysis
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Abstract

This paper derives a general superconvergence result for finite element approximations of the Navier-Stokes problem by using a least-squares surface fitting method proposed and analyzed recently by Wang for the standard Galerkin method. The superconvergence result is based on some regularity assumption for the Navier-Stokes problem and is applicable to any finite element method with quasi-uniform meshes. The method is demonstrated to give a convergent scheme for finite element spaces which fail to satisfy the well-known uniform inf-sup condition of Brezzi and Babuska.