A Parallel Finite Element Variational Multiscale Method Based on Fully Overlapping Domain Decomposition for Incompressible Flows

作者：Shang, Yueqiang^*

来源：Numerical Methods for Partial Differential Equations, 2015, 31(3): 856-875.

DOI：10.1002/num.21923

• Incompressible flow
• Navier-Stokes equations
• finite element
• variational multiscale method
• parallel algorithm

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.

• 出版日期2015-5
• 单位西南大学