Global superconvergence for blending surfaces by boundary penalty plus hybrid FEMs

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	Global superconvergence for blending surfaces by boundary penalty plus hybrid FEMs
	Li, ZC ; Yan, NN
	2001-10-01
发表期刊	APPLIED NUMERICAL MATHEMATICS
ISSN	0168-9274
卷号	39 期号:1 页码:61-85
摘要	In this paper, consider biharmonic equations and 31) blending surfaces, and choose the bi-cubic Hermite elements to seek their approximate solutions. We pursue not only the global superconvergence originated in Lin and his colleagues (Lin, 1994; Lin and Luo, 1995; Lin and Yan, 1996), but also better numerical stability. The boundary penalty plus hybrid integrals are employed to satisfy the normal derivative boundary conditions. Compared with the penalty finite methods (BP-FEM) of bi-cubic Hermite elements in (Li, 1998, 1999; Li and Chang, 1999), the merit of the new methods in this paper is reduction of a's values thus to improve numerical stability. Suppose that the solution domain Omega can be split into small rectangles square (ij). The global superconvergence O(h(2.5)) and O(h(3.5)) in H-2 norms are achieved for quasiuniform and uniform square (ij), respectively. Both cases yield the optimal condition number O(h(-4)), compared with O(h(-6)) and O(h(-8)) in (Li, 1999; Li and Chang, 1999). This is an important improvement of stability for biharmonic solutions. However, for 31) blending surfaces, only the global superconvergence O(h3) is achieved for uniform square (ij). Morever, numerical experiments are provided for biharmonic equations to support the high superconvergence O(h(3.5)) involving the natural boundary condition for uniform square (ij) with parameter mu epsilon [0, 1] This paper manifests a great flexibility of global superconvegence in applications. (C) 2001 IMACS. Published by Elsevier Science B.V. All rights reserved.
关键词	blending surfaces biharmonic equation bi-cubic Hermite element boundary penalty methods boundary hybrid techniques superconvergence stability
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000171204800005
出版者	ELSEVIER SCIENCE BV
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/16238
专题	中国科学院数学与系统科学研究院
通讯作者	Li, ZC
作者单位	1.Natl Sun Yat Sen Univ, Dept Math Appl, Kaohsiung 80242, Taiwan 2.Acad Sinica, Acad Math & Syst Sci, Inst Syst Sci, Beijing 10080, Peoples R China
推荐引用方式 GB/T 7714	Li, ZC,Yan, NN. Global superconvergence for blending surfaces by boundary penalty plus hybrid FEMs[J]. APPLIED NUMERICAL MATHEMATICS,2001,39(1):61-85.
APA	Li, ZC,&Yan, NN.(2001).Global superconvergence for blending surfaces by boundary penalty plus hybrid FEMs.APPLIED NUMERICAL MATHEMATICS,39(1),61-85.
MLA	Li, ZC,et al."Global superconvergence for blending surfaces by boundary penalty plus hybrid FEMs".APPLIED NUMERICAL MATHEMATICS 39.1(2001):61-85.