The minimal conforming 𝐻^{𝑘} finite element spaces on 𝑅ⁿ rectangular grids

Hu, Jun; Zhang, Shangyou

doi:10.1090/S0025-5718-2014-02871-8

The minimal conforming $H^k$ finite element spaces on $R^n$ rectangular grids
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by Jun Hu and Shangyou Zhang;

Math. Comp. 84 (2015), 563-579

DOI: https://doi.org/10.1090/S0025-5718-2014-02871-8

Published electronically: August 14, 2014

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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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