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A Divergence Free Weak Virtual Element Method for the Stokes Problem on Polytopal Meshes

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Abstract

Some virtual element methods on polytopal meshes for the Stokes problem are proposed and analyzed. The pressure is approximated by discontinuous polynomials, while the velocity is discretized by H(div) virtual elements enriched with some tangential polynomials on the element boundaries. A weak symmetric gradient of the velocity is computed using the corresponding degree of freedoms. The main feature of the method is that it exactly preserves the divergence free constraint, and therefore the error estimates for the velocity does not explicitly depend on the pressure.

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Author information

Authors and Affiliations

  1. Beijing Institute for Scientific and Engineering Computing, Beijing University of Technology, Beijing, 100124, China

    Long Chen

  2. Department of Mathematics, University of California at Irvine, Irvine, CA, 92697, USA

    Long Chen

  3. Jiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing, 210023, China

    Feng Wang

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  1. Long Chen
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  2. Feng Wang
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Correspondence to Feng Wang.

Additional information

Long Chen was supported by the National Science Foundation (NSF) DMS-1418934 and in part by the Sea Poly Project of Beijing Overseas Talents, and Feng Wang was supported by National Natural Science Foundation of China (Grant Nos. 11371199, 11371198, 11301275) and the Fund of Overseas Research and Training Program for Excellent Young and Middle-aged Teachers and Presidents in Universities and Colleges of Jiangsu.

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Chen, L., Wang, F. A Divergence Free Weak Virtual Element Method for the Stokes Problem on Polytopal Meshes. J Sci Comput 78, 864–886 (2019). https://doi.org/10.1007/s10915-018-0796-5

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  • DOI: https://doi.org/10.1007/s10915-018-0796-5

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