Overlapping nonmatching grid mortar element methods for elliptic problems

被引:39
作者
Cai, XC [1 ]
Dryja, M
Sarkis, M
机构
[1] Univ Colorado, Dept Comp Sci, Boulder, CO 80309 USA
[2] Inst Comp Applicat Sci & Engn, Boulder, CO 80309 USA
[3] Warsaw Univ, Fac Math Info & Mech, Warsaw, Poland
[4] Worcester Polytech Inst, Dept Math Sci, Worcester, MA 01609 USA
关键词
nonmatching grid; finite element; mortar projection; overlapping domain decomposition; elliptic equations; Schwarz preconditioner;
D O I
10.1137/S0036142997323582
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
In the first part of the paper, we introduce an overlapping mortar finite element method for solving two-dimensional elliptic problems discretized on overlapping nonmatching grids. We prove an optimal error bound and estimate the condition numbers of certain overlapping Schwarz preconditioned systems for the two-subdomain case. We show that the error bound is independent of the size of the overlap and the ratio of the mesh parameters. In the second part, we introduce three additive Schwarz preconditioned conjugate gradient algorithms based on the trivial and harmonic extensions. We provide estimates for the spectral bounds on the condition numbers of the preconditioned operators. We show that although the error bound is independent of the size of the overlap, the condition number does depend on it. Numerical examples are presented to support our theory.
引用
收藏
页码:581 / 606
页数:26
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