Local and Parallel Finite Element Algorithms Based on Two-Grid Discretizations for Nonlinear Problems
Local and Parallel Finite Element Algorithms Based on Two-Grid Discretizations for Nonlinear Problems
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DOI：
10.1023/a:1012284322811
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发表时间：
2001-05
影响因子：
1.7
通讯作者：
Jinchao Xu;Aihui Zhou
中科院分区：
文献类型：
--
作者：
Jinchao Xu;Aihui Zhou
本文提出并分析了二维和三维非线性椭圆边值问题的局部和并行离散及自适应有限元算法。其主要技术是在粗网格上使用标准有限元离散化来近似低频，然后在细网格上应用一些线性化离散化，以通过一些局部/并行程序来校正所产生的残差（主要包含高频）。分析这些方法的理论工具是本文得到的一般形状规则网格上有限元解的一些局部先验和后验误差估计。
In this paper, some local and parallel discretizations and adaptive finite element algorithms are proposed and analyzed for nonlinear elliptic boundary value problems in both two and three dimensions. The main technique is to use a standard finite element discretization on a coarse grid to approximate low frequencies and then to apply some linearized discretization on a fine grid to correct the resulted residual (which contains mostly high frequencies) by some local/parallel procedures. The theoretical tools for analyzing these methods are some local a priori and a posteriori error estimates for finite element solutions on general shape-regular grids that are also obtained in this paper.