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A Parallel Subgrid Stabilized Finite Element Method Based on Two-Grid Discretization for Simulation of 2D/3D Steady Incompressible Flows

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Abstract

Based on domain decomposition and two-grid discretization, a parallel subgrid stabilized finite element method for simulation of 2D/3D steady convection dominated incompressible flows is proposed and analyzed. In this method, a subgrid stabilized nonlinear Navier–Stokes problem is first solved on a coarse grid where the stabilization term is based on an elliptic projection defined on the same coarse grid, and then corrections are calculated in overlapped fine grid subdomains by solving a linearized problem. By the technical tool of local a priori estimate for finite element solution, error bounds of the approximate solution are estimated. Algorithmic parameter scalings of the method are derived. Numerical results are also given to demonstrate the effectiveness of the method.

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Acknowledgments

This work was supported by the Natural Science Foundation of China (No. 11361016), the Project Sponsored by the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry, the Scientific Research Foundation of Southwest University, Fundamental Research Funds for the Central Universities (No. SWU113095), and the Science and Technology Foundation of Guizhou Province, China (No. [2013]2212). The authors appreciate the valuable comments and suggestions made by the reviewer which led to an improvement of the paper.

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  1. School of Mathematics and Statistics, Southwest University, Chongqing, 400715, People’s Republic of China

    Yueqiang Shang

  2. School of Mathematics and Computer Science, Guizhou Normal University, Guiyang, 550001, People’s Republic of China

    Shumei Huang

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  1. Yueqiang Shang
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  2. Shumei Huang
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Correspondence to Yueqiang Shang.

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Shang, Y., Huang, S. A Parallel Subgrid Stabilized Finite Element Method Based on Two-Grid Discretization for Simulation of 2D/3D Steady Incompressible Flows. J Sci Comput 60, 564–583 (2014). https://doi.org/10.1007/s10915-013-9806-9

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