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Local tangential lifting virtual element method for the diffusion–reaction equation on the non-flat Voronoi discretized surface

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Abstract

In this paper, we propose the surface virtual element method (SVEM) combining with the local tangential lifting technique (LTL) to solve the diffusion–reaction (DR) equation on the non-flat Voronoi discretized surface embedded in \({\mathbb {R}}^3\). It has been a challenge on how to design the efficient numerical method to treat the non-flat discretized surface in comparison with the easy construction of flat discretized surface. Limited to the linear virtual element space, we derive the computable virtual element form of the non-flat Voronoi discretized surface by lifting the Voronoi element into the tangential plane. We demonstrate that this method developed here presents a good numerical simulation on a wide variety of polygonal discretized surfaces. Finally, numerical experiments are carried out to show the efficiency of the proposed method.

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Authors and Affiliations

  1. College of Mathematics and System Science, Xinjiang University, Urumqi, 830046, People’s Republic of China

    Jingwei Li, Xinlong Feng & Yinnian He

  2. Laboratory of Mathematics and Complex Systems and School of Mathematical Sciences, Beijing Normal University, Beijing, 100875, People’s Republic of China

    Jingwei Li

  3. School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, 710049, People’s Republic of China

    Yinnian He

Authors
  1. Jingwei Li
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  2. Xinlong Feng
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  3. Yinnian He
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Correspondence to Jingwei Li.

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This work is in part supported by the Excellent Doctor Innovation Program of Xinjiang University (No. XJUBSCX-2017006), China Postdoctoral Science Foundation (No. 2021M700476) and the NSF of China (Nos. 11671345, 11362021, 61962056).

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Li, J., Feng, X. & He, Y. Local tangential lifting virtual element method for the diffusion–reaction equation on the non-flat Voronoi discretized surface. Engineering with Computers 38, 5297–5307 (2022). https://doi.org/10.1007/s00366-021-01595-1

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  • DOI: https://doi.org/10.1007/s00366-021-01595-1

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