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	A discrete Helmholtz decomposition with Morley finite element functions and the optimality of adaptive finite element schemes
	Carstensen, Carsten ; Gallistl, Dietmar ; Hu, Jun
	2014
关键词	Discrete Helmholtz decomposition Morley element Kirchhoff-Love plate problem Optimality PLATE-BENDING PROBLEMS BOUNDARY-CONDITIONS ERROR ANALYSIS CONVERGENCE EQUATIONS
英文摘要	The discrete reliability of a finite element method is a key ingredient to prove optimal convergence of an adaptive mesh-refinement strategy and requires the interchange of a coarse triangulation and some arbitrary refinement of it. One approach for this is the careful design of an intermediate triangulation with one-level refinements and with the remaining difficulty to design some interpolation operator which maps a possibly nonconforming approximation into the finite element space based on the finer triangulation. This paper enfolds the second possibility of some novel discrete Helmholtz decomposition for the nonconforming Morley finite element method. This guarantees the optimality of a standard adaptive mesh-refining algorithm for the biharmonic equation. Numerical examples illustrate the crucial dependence of the bulk parameter and the surprisingly short pre-asymptotic range of the adaptive Morley finite element method. (C) 2014 Elsevier Ltd. All rights reserved.; Mathematics, Applied; SCI(E); EI; 1; ARTICLE; cc@math.hu-berlin.de; gallistl@math.hu-berlin.de; hujun@math.pku.edu.cn; 12,SI; 2167-2181; 68
语种	英语
出处	SCI ; EI
出版者	computers mathematics with applications
内容类型	其他
源URL	[http://hdl.handle.net/20.500.11897/207097]
专题	数学科学学院
推荐引用方式 GB/T 7714	Carstensen, Carsten,Gallistl, Dietmar,Hu, Jun. A discrete Helmholtz decomposition with Morley finite element functions and the optimality of adaptive finite element schemes. 2014-01-01.

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