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Journal of Scientific Computing

Erschienen in:

01.01.2015

Superconvergence Analysis for Linear Tetrahedral Edge Elements

verfasst von: Yunqing Huang, Jichun Li, Chao Wu, Wei Yang

Erschienen in: Journal of Scientific Computing | Ausgabe 1/2015

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Abstract

Back in 1992, Monk (Numer Math 63: 243–261, 1992) found that the numerical solution of time-harmonic Maxwell equations shows a superconvergence result \(O(h^2)\) in the discrete maximum norm when the problem is solved by Nédé1ec’s first type linear tetrahedral elements (i.e., the so-called edge elements). However, Monk did not provide any theoretical investigation of this superconvergence phenomenon. Since then, superconvergence analysis has been carried out for edge elements on hexahedral grids and triangular grids. Until now, the theoretical justification of the superconvergence phenomenon for linear edge elements on tetrahedral grids is still open (Monk in Finite element methods for Maxwell’s equations. Oxford University Press, Oxford, 2003, p.188) . The paper is motivated by this open issue. Our major goal of this paper is to fill this gap by providing a delicate theoretical analysis of this superconvergence phenomenon. We further provide some numerical results to demonstrate this phenomenon.

Vorheriger Artikel Finite Difference Schemes for the Cauchy–Navier Equations of Elasticity with Variable Coefficients

Nächster Artikel Decay Properties for the Numerical Solutions of a Partial Differential Equation with Memory

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Titel: Superconvergence Analysis for Linear Tetrahedral Edge Elements
verfasst von: Yunqing Huang
Jichun Li
Chao Wu
Wei Yang
Publikationsdatum: 01.01.2015
Verlag: Springer US
Erschienen in: Journal of Scientific Computing / Ausgabe 1/2015
Print ISSN: 0885-7474
Elektronische ISSN: 1573-7691
DOI: https://doi.org/10.1007/s10915-014-9848-7

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