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Quadratic immersed finite element spaces and their approximation capabilities

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Abstract

This paper discusses a class of quadratic immersed finite element (IFE) spaces developed for solving second order elliptic interface problems. Unlike the linear IFE basis functions, the quadratic IFE local nodal basis functions cannot be uniquely defined by nodal values and interface jump conditions. Three types of one dimensional quadratic IFE basis functions are presented together with their extensions for forming the two dimensional IFE spaces based on rectangular partitions. Approximation capabilities of these IFE spaces are discussed. Finite element solutions based on these IFE for representative interface problems are presented to further illustrate capabilities of these IFE spaces.

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Authors and Affiliations

  1. Department of Mathematics, Virginia Tech, USA

    Brian Camp & Tao Lin

  2. Department of Mathematics Sciences, University of Alberta, Canada and Northeastern University at Qinhuangdao, Qinhuangdao, Hebei, China

    Yanping Lin

  3. Department of Mathematics, City University of Hong Kong, Hong Kong, China

    Weiwei Sun

Authors
  1. Brian Camp
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  2. Tao Lin
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  3. Yanping Lin
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  4. Weiwei Sun
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Additional information

Communicated by Yuesheng Xu

Dedicated to the 60th birthday of Charles A. Micchelli

Mathematics subject classifications (2000)

65N15, 65N30, 65N50, 65Z05.

Yanping Lin: Supported by NSERC.

Weiwei Sun: This work was supported in part by a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China (project CityU 1141/01P).

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Camp, B., Lin, T., Lin, Y. et al. Quadratic immersed finite element spaces and their approximation capabilities. Adv Comput Math 24, 81–112 (2006). https://doi.org/10.1007/s10444-004-4139-8

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  • DOI: https://doi.org/10.1007/s10444-004-4139-8

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