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Two‐level finite element method with a stabilizing subgrid for the incompressible Navier–Stokes equations
Author(s) -
Nesliturk A. I.,
Aydın S. H.,
TezerSezgin M.
Publication year - 2008
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.1753
Subject(s) - finite element method , discretization , mathematics , piecewise linear function , galerkin method , pressure correction method , navier–stokes equations , piecewise , incompressible flow , mixed finite element method , compressibility , mathematical analysis , domain (mathematical analysis) , bubble , discontinuous galerkin method , extended finite element method , level set method , geometry , flow (mathematics) , physics , computer science , mechanics , segmentation , artificial intelligence , image segmentation , thermodynamics
We consider the Galerkin finite element method for the incompressible Navier–Stokes equations in two dimensions. The domain is discretized into a set of regular triangular elements and the finite‐dimensional spaces employed consist of piecewise continuous linear interpolants enriched with the residual‐free bubble functions. To find the bubble part of the solution, a two‐level finite element method with a stabilizing subgrid of a single node is described, and its application to the Navier–Stokes equation is displayed. Numerical approximations employing the proposed algorithm are presented for three benchmark problems. The results show that the proper choice of the subgrid node is crucial in obtaining stable and accurate numerical approximations consistent with the physical configuration of the problem at a cheap computational cost. Copyright © 2008 John Wiley & Sons, Ltd.