用于高度各向异性椭圆方程渐近保持方法的高纵横比各向异性有限元
数值分析
2013-02-19 v1
摘要
本工作致力于推广 [P. Degond, A. Lozinski, J. Narski, and C. Negulescu. An asymptotic-preserving method for highly anisotropic elliptic equations based on a micro-macro decomposition. J. Comput. Phys., 231(7):2724{2740, 2012] 中提出的针对高度各向异性椭圆方程的渐近保持 (Asymptotic Preserving) 方法。通过在渐近重构中引入稳定项，消除了该方法原有的局限性。此外，我们提出并测试了各向异性误差指示器和网格自适应算法，使得在达到指定精度时所需的网格点数大幅减少。报告的网格最大纵横比大于 500。
引用
@article{arxiv.1302.4269,
title = {Anisotropic finite elements with high aspect ratio for an Asymptotic Preserving method for highly anisotropic elliptic equation},
author = {Jacek Narski},
journal= {arXiv preprint arXiv:1302.4269},
year = {2013}
}