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Int. J. Numer. Anal. Mod., 6 (2009), pp. 147-160. |
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A domain decomposition method with Lagrange multiplier based on the pointwise matching condition Dudu Sun 1, Qiya Hu 2, Shi Shu 3 1 Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Graduate University of Chinese Academy of Sciences, Chinese Academy of Sciences, Beijing, China.2 Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China. 3 Department of Mathematics, Xiangtan University, Hunan Province, China. Received by the editors March 1, 2008 and, in revised form, May 22, 2008. Abstract
In this paper, we are concerned with a non-overlapping domain decomposition method with nonmatching grids. In this method, a new pointwise matching condition is used to define weak continuity of approximate solutions on the interface. The main merit of the new method is that numerical integrations can be avoided when calculating interface matrices. We derive an almost optimal error estimate of the resulting approximate solutions for two kinds of applicable situations. Some numerical experiments confirm the theoretical result. AMS subject classifications: 65F10, 65N30, 65N55 Key words: Domain decomposition, nonmatching grids, pointwise matching, error estimate. Email: sundudu@lsec.cc.ac.cn, hqy@lsec.cc.ac.cn, shushi@xtu.edu.cn |