Anisotropic Mesh Adaptation for Solution of Finite Element Problems Using Hierarchical Edge-Based Error Estimates
Anisotropic Mesh Adaptation for Solution of Finite Element Problems Using Hierarchical Edge-Based Error Estimates
复制标题
使用基于边缘的分层误差估计求解有限元问题的各向异性网格自适应
DOI：
10.1007/978-3-642-04319-2_34
复制
发表时间：
2009
期刊：
影响因子：
3.7
通讯作者：
Y. Vassilevski
中科院分区：
文献类型：
--
作者：
A. Agouzal;K. Lipnikov;Y. Vassilevski
提出了一种新的网格生成技术，使插值和离散误差及其梯度最小化。该方法的关键要素是从基于边缘的误差估计构建空间度量。对于N h三角形网格，误差与\（N h^{-1}\）成正比，误差梯度与\（N h^{-1/2}\）成正比，这是最优渐近。数值实验验证了该方法的有效性。
We present a new technology for generating meshes minimizing the interpolation and discretization errors or their gradients. The key element of this methodology is construction of a space metric from edge-based error estimates. For a mesh with N h triangles, the error is proportional to \(N_h^{-1}\) and the gradient of error is proportional to \(N_h^{-1/2}\) which are the optimal asymptotics. The methodology is verified with numerical experiments.