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Two‐grid variational multiscale algorithms for the stationary incompressible Navier‐Stokes equations with friction boundary conditions
Author(s) -
Qiu Hailong,
Mei Liquan,
Zhang Yongchao
Publication year - 2017
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.22118
Subject(s) - grid , convergence (economics) , mathematics , compressibility , nonlinear system , boundary (topology) , navier–stokes equations , partial differential equation , stability (learning theory) , algorithm , mathematical analysis , computer science , geometry , mechanics , physics , quantum mechanics , machine learning , economics , economic growth
Two‐grid variational multiscale (VMS) algorithms for the incompressible Navier‐Stokes equations with friction boundary conditions are presented in this article. First, one‐grid VMS algorithm is used to solve this problem and some error estimates are derived. Then, two‐grid VMS algorithms are proposed and analyzed. The algorithms consist of nonlinear problem on coarse grid and linearized problem (Stokes problem or Oseen problem) on fine grid. Moreover, the stability and convergence of the present algorithms are established. Finally, Numerical results are shown to confirm the theoretical analysis. © 2016 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 546–569, 2017