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A Stabilized Characteristic-Nonconforming Finite Element Method for Time-Dependent Incompressible Navier–Stokes Equations

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Abstract

In this paper, we study a stabilized characteristic-nonconforming finite element method to solve the time-dependent incompressible Navier–Stokes equations. The characteristic scheme is used to deal with advection term and temporal differentiation, which avoid some difficulties caused by trilinear terms. The space discretization utilizes the nonconforming lowest equal-order pair of mixed finite elements (i.e. \(\textit{NCP}_1-{\mathbf {P}}_1\)). The stability analysis and optimal-order error estimates for velocity and pressure are presented. Numerical results are also provided to verify theory analysis.

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Acknowledgments

This article is supported by the National Nature Foundation of China (No. 11401422), the Soft Science Foundation of shanxi (No. 2014041007-3), and the Provincial Natural Science Foundation of Shanxi (No. 2015011001, 2014011005-4).

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Authors and Affiliations

  1. The College of Mathematics, Taiyuan University of Technology, Taiyuan, 030024, China

    Huiyong Jia & Hongen Jia

  2. The College of Science, Xian Jiaotong University, Xi’an, 710049, China

    Kaitai Li

Authors
  1. Huiyong Jia
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  2. Kaitai Li
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  3. Hongen Jia
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Correspondence to Hongen Jia.

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Communicated by Ahmad Izani Md. Ismail.

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Jia, H., Li, K. & Jia, H. A Stabilized Characteristic-Nonconforming Finite Element Method for Time-Dependent Incompressible Navier–Stokes Equations. Bull. Malays. Math. Sci. Soc. 41, 207–230 (2018). https://doi.org/10.1007/s40840-015-0272-4

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  • DOI: https://doi.org/10.1007/s40840-015-0272-4

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