Variational mesh adaptation II: error estimates and monitor functions
Variational mesh adaptation II: error estimates and monitor functions
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DOI：
10.1016/s0021-9991(02)00040-2
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发表时间：
2003-01-20
影响因子：
4.1
通讯作者：
Sun, WW
中科院分区：
文献类型：
--
作者：
Huang, WZ;Sun, WW
变分网格自适应方法成功的关键是定义一个控制网格自适应的监控函数。在本文中，我们研究的监测功能的选择变分自适应网格方法在以前的工作[J。174（2001）924]。基于有限元插值理论得到的插值误差的渐近估计，定义了标量矩阵和非标量矩阵两类监控函数。适应强度参数的选择也讨论了这些监控功能。对于满足正则性和等分布条件的自适应网格，得到了插值误差的渐近界。二维数值结果验证了理论研究结果。(C)2002 Elsevier Science B.V.保留所有权利。
The key to the success of a variational mesh adaptation method is to define a proper monitor function which controls mesh adaptation. In this paper we study the choice of the monitor function for the variational adaptive mesh method developed in the previous work [J. Comput. Phys. 174 (2001) 924]. Two types of monitor functions, scalar matrix and non-scalar matrix ones, are defined based on asymptotic estimates of interpolation error obtained using the interpolation theory of finite element methods. The choice of the adaptation intensity parameter is also discussed for each of these monitor functions. Asymptotic bounds on interpolation error are obtained for adaptive meshes that satisfy the regularity and equidistribution conditions. Two-dimensional numerical results are given to verify the theoretical findings. (C) 2002 Elsevier Science B.V. All rights reserved.