A C0 Linear Finite Element Method for Biharmonic Problems
نویسندگان
چکیده
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 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 C0 interior penalty method is given. 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. B Qingsong Zou [email protected] Hailong Guo [email protected] Zhimin Zhang [email protected]; [email protected] 1 Department of Mathematics, Wayne State University, Detroit, MI 48202, USA 2 Present Address: Department of Mathematics, University of California, Santa Barbara, CA 93106, USA 3 Beijing Computational Science Research Center, Beijing 100193, China 4 School of Data and Computer Science and Guangdong Province Key Laboratory of Computational Science, Sun Yat-sen University, Guangzhou 510275, China
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تاریخ انتشار 2017