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Flexible piecewise approximations based on partition of unity

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Abstract

In this paper, we study a flexible piecewise approximation technique based on the use of the idea of the partition of unity. The approximations are piecewisely defined, globally smooth up to any order, enjoy polynomial reproducing conditions, and satisfy nodal interpolation conditions for function values and derivatives of any order. We present various properties of the approximations, that are desirable properties for optimal order convergence in solving boundary value problems.

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Authors and Affiliations

  1. Department of Mathematics, University of Iowa City, IA, 52242, USA

    Weimin Han

  2. Department of Mechanical Engineering, Northwestern University, Evanston, IL, 60208, USA

    Wing Kam Liu

Authors
  1. Weimin Han
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  2. Wing Kam Liu
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Corresponding author

Correspondence to Weimin Han.

Additional information

Communicated by Z. Wu and B.Y.C. Hon

AMS subject classification

65N30, 65D05

Weimin Han: Corresponding author. The work of this author was partially supported by NSF under grant DMS-0106781.

Wing Kam Liu: The work of this author was supported by NSF.

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Han, W., Liu, W.K. Flexible piecewise approximations based on partition of unity. Adv Comput Math 23, 191–199 (2005). https://doi.org/10.1007/s10444-004-1810-z

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  • DOI: https://doi.org/10.1007/s10444-004-1810-z

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