A Cubic<i> H</i> <sup>3</sup>-Nonconforming Finite Element

Jun Hu; Shangyou Zhang

doi:10.1007/s42967-019-0009-8

Communications on Applied Mathematics and Computation ›› 2019, Vol. 1 ›› Issue (1) : 81-100. DOI: 10.1007/s42967-019-0009-8

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A Cubic H ³-Nonconforming Finite Element

Jun Hu¹^,a ,
Shangyou Zhang²

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Abstract

The lowest degree of polynomial for a finite element to solve a 2kth-order elliptic equation is k. The Morley element is such a finite element, of polynomial degree 2, for solving a fourth-order biharmonic equation. We design a cubic $H^3$-nonconforming macro-element on two-dimensional triangular grids, solving a sixth-order tri-harmonic equation. We also write down explicitly the 12 basis functions on each macro-element. A convergence theory is established and verified by numerical tests.

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Jun Hu, Shangyou Zhang. A Cubic H ³-Nonconforming Finite Element. Communications on Applied Mathematics and Computation, 2019, 1(1): 81‒100 https://doi.org/10.1007/s42967-019-0009-8