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A two‐level variational multiscale method for incompressible flows based on two local Gauss integrations
Author(s) -
Li Ying,
Mei Liquan,
Li Yueqiu,
Zhao Ke
Publication year - 2013
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.21785
Subject(s) - gauss , mathematics , computation , grid , finite element method , compressibility , projection (relational algebra) , operator (biology) , projection method , stability (learning theory) , mathematical analysis , mathematical optimization , algorithm , geometry , computer science , dykstra's projection algorithm , physics , biochemistry , chemistry , quantum mechanics , repressor , machine learning , gene , transcription factor , thermodynamics
In this article, a two‐level variational multiscale method for incompressible flows based on two local Gauss integrations is presented. We solve the Navier–Stokes problem on a coarse mesh using finite element variational multiscale method based on two local Gauss integrations, then seek a fine grid solution by solving a linearized problem on a fine grid. In computation, we use the two local Gauss integrations to replace the projection operator without adding any variables. Stability analysis is performed, and error estimates of the method are derived. Finally, a series of numerical experiments are also given, which confirm the theoretical analysis and demonstrate the efficiency of the new method. © 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013