Cascadic multigrid methods for parabolic problems

被引：0
作者：
Qiang Du
PingBing Ming
机构：
[1] Pennsylvania State University,Department of Mathematics
[2] Chinese Academy of Sciences,LSEC, Institute of Computational Mathematics and Scientific/Engineering Computing, AMSS
来源：
Science in China Series A: Mathematics | 2008年 / 51卷
关键词：
cascadic multigrid method; parabolic problem; finite element methods; backward Euler scheme; smoother; stability; optimal error order; optimal complexity; 65N30; 65N55; 65F10;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In this paper, we consider the cascadic multigrid method for a parabolic type equation. Backward Euler approximation in time and linear finite element approximation in space are employed. A stability result is established under some conditions on the smoother. Using new and sharper estimates for the smoothers that reflect the precise dependence on the time step and the spatial mesh parameter, these conditions are verified for a number of popular smoothers. Optimal error bounds are derived for both smooth and non-smooth data. Iteration strategies guaranteeing both the optimal accuracy and the optimal complexity are presented.
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页码：1415 / 1439
页数：24
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