Anisotropic interpolation error estimates via orthogonal expansions
type: Item
instance of: scholarly article
title: Anisotropic interpolation error estimates via orthogonal expansions
zbMATH Open document ID: 1269.65016
author: Shipeng Mao
author: Mingxia Li
published in: Central European Journal of Mathematics
publication date: 2013-04-08T00:00:00Z
review text: This paper defines an anisotropic interpolation operator on a reference square considering polynomial spaces of arbitrary degree. Its construction is based on orthogonal expansions with respect to Lobatto polynomials. An interpolation property is then proved. A standard technique [\textit{T. Apel}, Anisotropic finite elements: Local estimates and applications. Advances in Numerical Mathematics, Leipzig: Teubner (1999; Zbl 0934.65121), Theorem 2.6] then implies an interpolation result for a family of affine equivalent (parallelogram) meshes satisfying (i) a maximum angle condition and (ii) a coordinate system condition: the sine of the angle between the longest side and the \(x\)-axis is bounded by a constant and the aspect ratio. Note that such a family of meshes does not need necessarily to be regular. This result is then generalized to three dimensions and a similar anisotropic interpolation result for Lagrange hexahedral (parallelepiped) elements is proved.
Mathematics Subject Classification ID: 65D05
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 41A05
zbMATH DE Number: 6151354
zbMATH Keywords: quadrilateral
zbMATH Keywords: hexahedron
zbMATH Keywords: mesh
zbMATH Keywords: Lobatto polynomials
zbMATH Keywords: maximum angle condition
zbMATH Keywords: coordinate system condition
zbMATH Keywords: anisotropic interpolation operator
zbMATH Keywords: finite elements
reviewed by: Tomas Vejchodsky
MaRDI profile type: Publication
full work available at URL: s11533-013-0203-2
OpenAlex ID: W2143899726
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DOI: 10.2478/S11533-013-0203-2
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description: scientific article; zbMATH DE number 6151354