论非常规有限元与其常规对偶有限元的谱等价性

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基金项目: 国家自然科学基金资助项目(19901018)

On the Spectral Equivalence of Unconventional Finite Elements and Their Conventional Relatives

Department of Applied Mathematics, Shanghai Jiaotong University, Shanghai 200240, P R China

摘要: 以一个广义协调元为例证明了非常规有限元与其常规对偶有限元刚度矩阵的谱等价性。该结果对非常规有限元的区域分解并行算法研究有重要作用。
- 非常规有限元 /
- 广义协调元 /
- 谱等价
Abstract: With a generalized conforming element as a typical example, the spectral equivalence of unconventional finite elements and their conventional relatives is proved. This result is very important for the construction of domain decomposition parallel algorithms for unconventional finite elements.
- unconventional finite element /
- generalized conforming element /
- spectral equivalence

[1]	Chan T F, Mathew T.Domain decomposition algorithms[J].Acta Numerica,1994,2;61-143.
[2]	Xu J C.Iterative methods by space decomposition and subspace correction[J].SIAM Review,1992,34(3);581-613.
[3]	Xu J C, Zou J.Non-overlapping domain decomposition methods[J].SIAM Review,1998,40(4);857-914.
[4]	Ciarlet P G.The Finite Element Method for Elliptic Problem[M].Amsterdam-New York-Oxford:North-Holland,1978.
[5]	龙驭球,辛克贵.广义协调元[J].土木工程学报,1987,1(1);1-14.
[6]	石钟慈,陈绍春.九参数广义协调元的收敛性[J].计算数学,1991,13(2);193-203.
[7]	龙驭球.新型有限元引论[M].北京;清华大学出版社,1992.
[8]	陈绍春,石钟慈.构造单元刚度矩阵的双参数法[J].计算数学,1991,13(3);286-296.
[9]	Brenner S C.A two-level additive preconditioner for nonconforming plate elements[J].Numer Math,1996,72(3);419-447.
[10]	谢正辉.Domain decomposition and multigrid methods for nonconforming plate elements[D].博士论文.北京;中科院计算数学研究所,1996.
[11]	Bramble J H, Pasciak J E, Schatz A H.The construction of preconditioners for elliptic problems by substructuring,Ⅰ[J].Math Comp,1986,47(1);102-134.