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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The first author is supported by the National Natural Science Foundation of China (Nos. 11271035, 91430213, 11421101).
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Hu, J., Zhang, S. A Cubic H3-Nonconforming Finite Element. Commun. Appl. Math. Comput. 1, 81–100 (2019). https://doi.org/10.1007/s42967-019-0009-8
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DOI: https://doi.org/10.1007/s42967-019-0009-8