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In general $n$-dimensional simplicial meshes, we propose a family of interior penalty nonconforming finite element methods for $2m$-th order partial differential equations, where $m \geq 0$ and $n \geq 1$.
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Jun Hu and Shangyou Zhang, The minimal conforming H k H^{k} finite element spaces on ℛ n \mathcal{R}^{n} rectangular grids , Mathematics of Computation 84
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Dietmar Gallistl, Stable splitting of polyharmonic operators by generalized Stokes systems , Mathematics of Computation 86
2017
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Shuonan Wu and Jinchao Xu, Nonconforming finite element spaces for 2 m 2m -th order partial differential equations on ℝ n \mathbb{R}^{n} simplicial grids when m = n + 1 m=n+1 , Mathematics of Computation 88
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2009
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Shipeng Mao and Zhong Ci Shi, On the error bounds of nonconforming finite elements , Science China Mathematics 53
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T. Gudi and M. Neilan, An interior penalty method for a sixth-order elliptic equation , IMA Journal of Numerical Analysis 31
2011
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Cheng. Wang and Steven M Wise, An energy stable and convergent finite-difference scheme for the modified phase field crystal equation , SIAM Journal on Numerical Analysis 49
2011
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L Beirão da Veiga, Franco Brezzi, Andrea Cangiani, Gianmarco Manzini, L Donatella Marini, and Alessandro Russo, Basic principles of virtual element methods , Mathematical Models and Methods in Applied Sciences 23
2013
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Shibin Dai and Keith Promislow, Geometric evolution of bilayers under the functionalized Cahn–Hilliard equation , Proceedings of the Royal Society A, vol. 469, The Royal Society, 2013, p. 20120505
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Ming Wang and Jinchao Xu, Minimal finite element spaces for 2 m 2m -th-order partial differential equations in ℝ n \mathbb{R}^{n} , Mathematics of Computation 82
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2014
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2019
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2020
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2020
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2022
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2081
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