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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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The minimal conforming $H^k$ finite element spaces on $R^n$ rectangular grids
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by Jun Hu and Shangyou Zhang PDF
Math. Comp. 84 (2015), 563-579 Request permission


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:
  • Shangyou Zhang
  • Affiliation: Department of Mathematical Sciences, University of Delaware, Newark, Delawre 19716
  • MR Author ID: 261174
  • Email:
  • 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.
  • © Copyright 2014 American Mathematical Society
  • Journal: Math. Comp. 84 (2015), 563-579
  • MSC (2010): Primary 65N30
  • DOI:
  • MathSciNet review: 3290955