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Some error analysis on virtual element methods

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Abstract

Some error analyses on virtual element methods (VEMs) including inverse inequalities, norm equivalence, and interpolation error estimates are developed for polygonal meshes, each element of which admits a virtual quasi-uniform triangulation. This sub-mesh regularity covers the usual ones used for theoretical analysis of VEMs, and the proofs are presented by means of standard technical tools in finite element methods.

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Acknowledgements

We thank the referees for valuable suggestions and comments which improved an early version of the paper. The first author was supported by the National Science Foundation (NSF) DMS-1418934 and in part by the Sea Poly Project of Beijing Overseas Talents. The second author was partially supported by NSFC (Grant No. 11571237).

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Authors and Affiliations

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

    Long Chen

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

    Long Chen

  3. School of Mathematical Sciences, MOE-LSC, Shanghai Jiao Tong University, Shanghai, 200240, China

    Jianguo Huang

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  1. Long Chen
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  2. Jianguo Huang
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Correspondence to Jianguo Huang.

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Chen, L., Huang, J. Some error analysis on virtual element methods. Calcolo 55, 5 (2018). https://doi.org/10.1007/s10092-018-0249-4

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