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2013 | 11 | 4 | 621-629
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Anisotropic interpolation error estimates via orthogonal expansions

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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.
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Bibliografia
  • [1] Acosta G., Apel T., Durán R.G., Lombardi A.L., Anisotropic error estimates for an interpolant defined via moments, Computing, 2008, 82(1), 1–9 http://dx.doi.org/10.1007/s00607-008-0259-1
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  • [6] Chen S., Zheng Y., Mao S., Anisotropic error bounds of Lagrange interpolation with any order in two and three dimensions, Appl. Math. Comput., 2011, 217(22), 9313–9321 http://dx.doi.org/10.1016/j.amc.2011.04.015
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  • [9] Hannukainen A., Korotov S., Křížek M., The maximum angle condition is not necessary for convergence of the finite element method, Numer. Math., 2012, 120(1), 79–88 http://dx.doi.org/10.1007/s00211-011-0403-2
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  • [12] Mao S., Shi Z., Error estimates of triangular finite elements under a weak angle condition, J. Comput. Appl. Math., 2009, 230(1), 329–331 http://dx.doi.org/10.1016/j.cam.2008.11.008
  • [13] Sansone G., Orthogonal Functions, Dover, New York, 1991
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bwmeta1.element.doi-10_2478_s11533-013-0203-2
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