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A parallel finite element variational multiscale method based on fully overlapping domain decomposition for incompressible flows
Author(s) -
Shang Yueqiang
Publication year - 2015
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.21923
Subject(s) - domain decomposition methods , finite element method , mathematics , gauss , mixed finite element method , domain (mathematical analysis) , extended finite element method , a priori and a posteriori , compressibility , partial differential equation , incompressible flow , pressure correction method , mathematical analysis , flow (mathematics) , geometry , physics , mechanics , philosophy , epistemology , quantum mechanics , thermodynamics
Based on fully overlapping domain decomposition and a recent variational multiscale method, a parallel finite element variational multiscale method for convection dominated incompressible flows is proposed and analyzed. In this method, each processor computes a local finite element solution in its own subdomain using a global mesh that is locally refined around its own subdomain, where a stabilization term based on two local Gauss integrations is adopted to stabilize the numerical form of the Navier–Stokes equations. Using the technical tool of local a priori estimate for the finite element solution, error bounds of the discrete solution are estimated. Algorithmic parameter scalings are derived. Numerical tests are also given to verify the theoretical predictions and demonstrate the effectiveness of the method. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 856–875, 2015