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Journal of Scientific Computing

Erschienen in:

20.07.2017

A \(C^0\) Linear Finite Element Method for Biharmonic Problems

verfasst von: Hailong Guo, Zhimin Zhang, Qingsong Zou

Erschienen in: Journal of Scientific Computing | Ausgabe 3/2018

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Abstract

In this paper, a \(C^0\) linear finite element method for biharmonic equations is constructed and analyzed. In our construction, the popular post-processing gradient recovery operators are used to calculate approximately the second order partial derivatives of a \(C^0\) linear finite element function which do not exist in traditional meaning. The proposed scheme is straightforward and simple. More importantly, it is shown that the numerical solution of the proposed method converges to the exact one with optimal orders both under \(L^2\) and discrete \(H^2\) norms, while the recovered numerical gradient converges to the exact one with a superconvergence order. Some novel properties of gradient recovery operators are discovered in the analysis of our method. In several numerical experiments, our theoretical findings are verified and a comparison of the proposed method with the nonconforming Morley element and \(C^0\) interior penalty method is given.

Vorheriger Artikel A Systematic Study on Weak Galerkin Finite Element Methods for Second Order Elliptic Problems

Nächster Artikel A Mass Conservative Scheme for Fluid–Structure Interaction Problems by the Staggered Discontinuous Galerkin Method

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Titel: A Linear Finite Element Method for Biharmonic Problems
verfasst von: Hailong Guo
Zhimin Zhang
Qingsong Zou
Publikationsdatum: 20.07.2017
Verlag: Springer US
Erschienen in: Journal of Scientific Computing / Ausgabe 3/2018
Print ISSN: 0885-7474
Elektronische ISSN: 1573-7691
DOI: https://doi.org/10.1007/s10915-017-0501-0

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