Journal article

A C-0 Linear Finite Element Method for Biharmonic Problems

Hailong Guo, Zhimin Zhang, Qingsong Zou

JOURNAL OF SCIENTIFIC COMPUTING | SPRINGER/PLENUM PUBLISHERS | Published : 2018

Abstract

In this paper, a C0 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 C0 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 L2 and discrete H2 norms, while the recovered numerical gradient converges to the exact one with a superconvergence order. Some novel properties of gradient recovery operators..

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University of Melbourne Researchers

Grants

Awarded by US National Science Foundation


Awarded by NSFC


Awarded by NASF


Awarded by NSF


Awarded by special project High performance computing of National Key Research and Development Program


Awarded by Guangdong Provincial NSF


Awarded by Fundamental Research Funds for the Central Universities


Funding Acknowledgements

H. Guo: The research of this author was supported in part by the US National Science Foundation through Grant DMS-1419040. Z. Zhang: The research of this author was supported in part by the following Grants: NSFC 11471031, NSFC 91430216, NASF U1530401, and NSF DMS-1419040. Q. Zou: The research of this author was supported in part by the following Grants: the special project High performance computing of National Key Research and Development Program 2016YFB0200604, NSFC 11571384, Guangdong Provincial NSF 2014A030313179, the Fundamental Research Funds for the Central Universities 16lgjc80.