Anisotropic interpolation error estimates via orthogonal expansions

Mingxia Li; Shipeng Mao

Open Mathematics (2013)

  • Volume: 11, Issue: 4, page 621-629
  • ISSN: 2391-5455

Abstract

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We prove anisotropic interpolation error estimates for quadrilateral and hexahedral elements with all possible shape function spaces, which cover the intermediate families, tensor product families and serendipity families. Moreover, we show that the anisotropic interpolation error estimates hold for derivatives of any order. This goal is accomplished by investigating an interpolation defined via orthogonal expansions.

How to cite

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Mingxia Li, and Shipeng Mao. "Anisotropic interpolation error estimates via orthogonal expansions." Open Mathematics 11.4 (2013): 621-629. <http://eudml.org/doc/269724>.

@article{MingxiaLi2013,
abstract = {We prove anisotropic interpolation error estimates for quadrilateral and hexahedral elements with all possible shape function spaces, which cover the intermediate families, tensor product families and serendipity families. Moreover, we show that the anisotropic interpolation error estimates hold for derivatives of any order. This goal is accomplished by investigating an interpolation defined via orthogonal expansions.},
author = {Mingxia Li, Shipeng Mao},
journal = {Open Mathematics},
keywords = {Error estimates; Anisotropic interpolation; Orthogonal expansions; quadrilateral; hexahedron; mesh; Lobatto polynomials; maximum angle condition; coordinate system condition; anisotropic interpolation operator; finite elements},
language = {eng},
number = {4},
pages = {621-629},
title = {Anisotropic interpolation error estimates via orthogonal expansions},
url = {http://eudml.org/doc/269724},
volume = {11},
year = {2013},
}

TY - JOUR
AU - Mingxia Li
AU - Shipeng Mao
TI - Anisotropic interpolation error estimates via orthogonal expansions
JO - Open Mathematics
PY - 2013
VL - 11
IS - 4
SP - 621
EP - 629
AB - We prove anisotropic interpolation error estimates for quadrilateral and hexahedral elements with all possible shape function spaces, which cover the intermediate families, tensor product families and serendipity families. Moreover, we show that the anisotropic interpolation error estimates hold for derivatives of any order. This goal is accomplished by investigating an interpolation defined via orthogonal expansions.
LA - eng
KW - Error estimates; Anisotropic interpolation; Orthogonal expansions; quadrilateral; hexahedron; mesh; Lobatto polynomials; maximum angle condition; coordinate system condition; anisotropic interpolation operator; finite elements
UR - http://eudml.org/doc/269724
ER -

References

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