A discrete Helmholtz decomposition with Morley finite element functions and the optimality of adaptive finite element schemes
A discrete Helmholtz decomposition with Morley finite element functions and the optimality of adaptive finite element schemes
复制标题
Morley有限元函数的离散亥姆霍兹分解和自适应有限元格式的最优性
DOI：
10.1016/j.camwa.2014.07.019
复制
发表时间：
2014-12-01
影响因子：
2.9
通讯作者：
Hu, Jun
中科院分区：
文献类型：
--
作者：
Carstensen, Carsten;Gallistl, Dietmar;Hu, Jun
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.
