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Journal of Scientific Computing

Erschienen in:

04.07.2016

Optimal Quadrilateral Finite Elements on Polygonal Domains

verfasst von: Hengguang Li, Qinghui Zhang

Erschienen in: Journal of Scientific Computing | Ausgabe 1/2017

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Abstract

We propose three quadrilateral mesh refinement algorithms to improve the convergence of the finite element method approximating the singular solutions of elliptic equations, which are due to the non-smoothness of the domain. These algorithms result in graded meshes consisting of convex and shape-regular quadrilaterals. With analysis in weighted spaces, we provide the selection criteria for the grading parameter, such that the optimal convergence rate can be recovered for the associated finite element approximation. Various numerical tests verify the theory. In addition to the bi-k elements, we also investigate the serendipity elements on the graded quadrilateral meshes in the numerical experiments.

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Titel: Optimal Quadrilateral Finite Elements on Polygonal Domains
verfasst von: Hengguang Li
Qinghui Zhang
Publikationsdatum: 04.07.2016
Verlag: Springer US
Erschienen in: Journal of Scientific Computing / Ausgabe 1/2017
Print ISSN: 0885-7474
Elektronische ISSN: 1573-7691
DOI: https://doi.org/10.1007/s10915-016-0242-5

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