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A weak Galerkin finite element method for the Oseen equations

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Abstract

In this paper, a weak Galerkin finite element method for the Oseen equations of incompressible fluid flow is proposed and investigated. This method is based on weak gradient and divergence operators which are designed for the finite element discontinuous functions. Moreover, by choosing the usual polynomials of degree i ≥ 1 for the velocity and polynomials of degree i − 1 for the pressure and enhancing the polynomials of degree i − 1 on the interface of a finite element partition for the velocity, this new method has a lot of attractive computational features: more general finite element partitions of arbitrary polygons or polyhedra with certain shape regularity, fewer degrees of freedom and parameter free. Stability and error estimates of optimal order are obtained by defining a weak convection term. Finally, a series of numerical experiments are given to show that this method has good stability and accuracy for the Oseen problem.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, 710049, China

    Xin Liu & Zhangxin Chen

  2. Department of Mathematics, Baoji University of Arts and Sciences, Baoji, 721013, China

    Jian Li

  3. Department of Mathematics, Shaanxi University of Sciences and Technology, Xi’an, 710021, China

    Jian Li

  4. Department of Chemical and Petroleum Engineering, Schulich School of Engineering, University of Calgary, 2500 University Drive N.W., Calgary, Alberta, T2N 1N4, Canada

    Zhangxin Chen

Authors
  1. Xin Liu
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  2. Jian Li
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  3. Zhangxin Chen
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Corresponding author

Correspondence to Zhangxin Chen.

Additional information

Communicated by: A. Zhou Research supported in part by NSF of China (No. 11371031), and the Key Projects of Baoji university of Arts and Sciences (No. ZK15040) and (No. ZK15033).

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Liu, X., Li, J. & Chen, Z. A weak Galerkin finite element method for the Oseen equations. Adv Comput Math 42, 1473–1490 (2016). https://doi.org/10.1007/s10444-016-9471-2

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  • DOI: https://doi.org/10.1007/s10444-016-9471-2

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