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Shang, Yueqiang

A parallel two-level finite element variational multiscale method for the Navier-Stokes equations. (English) Zbl 1278.65191

Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 84, 103-116 (2013).
Summary: A combination method of two-grid discretization approach with a recent finite element variational multiscale algorithm for simulation of the incompressible Navier-Stokes equations is proposed and analyzed. The method consists of a global small-scale nonlinear Navier-Stokes problem on a coarse grid and local linearized residual problems in overlapped fine grid subdomains, where the numerical form of the Navier-Stokes equations on the coarse grid is stabilized by a stabilization term based on two local Gauss integrations at element level and defined by the difference between a consistent and an under-integrated matrix involving the gradient of velocity. By 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.

Cited in 15 Documents

MSC:

65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs
76D05 Navier-Stokes equations for incompressible viscous fluids
76M10 Finite element methods applied to problems in fluid mechanics

Keywords:

Navier-Stokes equations; finite element; variational multiscale method; parallel algorithm; two-grid method

Software:

FreeFem++
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References:

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