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The minimal conforming $H^k$ finite element spaces on $R^n$ rectangular grids


Authors: Jun Hu and Shangyou Zhang
Journal: Math. Comp. 84 (2015), 563-579
MSC (2010): Primary 65N30
DOI: https://doi.org/10.1090/S0025-5718-2014-02871-8
Published electronically: August 14, 2014
MathSciNet review: 3290955
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Abstract: A family of $C^{k-1}$-$Q_{k}$ finite elements on $R^n$ rectangular grids is constructed. The finite element space is shown to be the full $C^{k-1}$-$Q_{k}$ space and possess the optimal order of approximation property. The polynomial degree is minimal in order to form such a $H^{k}$ finite element space. Numerical tests are provided for using the 2D $C^1$-$Q_{2}$ and $C^2$-$Q_{3}$ finite elements.


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Additional Information

Jun Hu
Affiliation: LMAM and School of Mathematical Sciences, Peking University, Beijing 100871, People’s Republic of China
MR Author ID: 714525
Email: hujun@math.pku.edu.cn

Shangyou Zhang
Affiliation: Department of Mathematical Sciences, University of Delaware, Newark, Delawre 19716
MR Author ID: 261174
Email: szhang@udel.edu

Keywords: Conforming finite element, rectangular grid
Received by editor(s): January 27, 2013
Received by editor(s) in revised form: May 10, 2013, June 6, 2013, and August 1, 2013
Published electronically: August 14, 2014
Additional Notes: The first author was supported by the NSFC Project 11271035, and in part by the NSFC Key Project 11031006.
Article copyright: © Copyright 2014 American Mathematical Society