A NEW DIVERGENCE-FREE INTERPOLATION OPERATOR WITH APPLICATIONS TO THE DARCY-STOKES-BRINKMAN EQUATIONS

doi:10.1137/090751049

	A NEW DIVERGENCE-FREE INTERPOLATION OPERATOR WITH APPLICATIONS TO THE DARCY-STOKES-BRINKMAN EQUATIONS
	Xu, Xuejun1 ; Zhang, Shangyou 2
	2010
发表期刊	SIAM JOURNAL ON SCIENTIFIC COMPUTING
ISSN	1064-8275
卷号	32 期号:2 页码:855-874
摘要	A new local interpolation operator, preserving the divergence, is constructed explicitly for the Hsieh-Clough-Tocher divergence-free element. A divergence-free finite element method is applied to the Darcy-Stokes-Brinkman flow in a mixed region of both free and porous media. The method is of optimal order as well for the Darcy flow as for the Stokes flow (which is not the case for most other finite elements). Compared to the existing nonconforming elements, the divergence-free element method provides a continuous solution for the velocity which is also an orthogonal projection within a Hilbert subspace of the true velocity. Numerical tests supporting the theory are presented.
关键词	mixed finite element Stokes equations Darcy's law Brinkman equations divergence-free element
DOI	10.1137/090751049
语种	英语
资助项目	State Key Laboratory of Scientific and Engineering Computing, CAS ; NSF of China[10731060] ; [2005CB321701]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000277837100018
出版者	SIAM PUBLICATIONS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/9642
专题	计算数学与科学工程计算研究所
通讯作者	Xu, Xuejun
作者单位	1.Chinese Acad Sci, Inst Computat Math, LSEC, Beijing 100080, Peoples R China 2.Univ Delaware, Dept Math Sci, Newark, DE 19716 USA
推荐引用方式 GB/T 7714	Xu, Xuejun,Zhang, Shangyou. A NEW DIVERGENCE-FREE INTERPOLATION OPERATOR WITH APPLICATIONS TO THE DARCY-STOKES-BRINKMAN EQUATIONS[J]. SIAM JOURNAL ON SCIENTIFIC COMPUTING,2010,32(2):855-874.
APA	Xu, Xuejun,&Zhang, Shangyou.(2010).A NEW DIVERGENCE-FREE INTERPOLATION OPERATOR WITH APPLICATIONS TO THE DARCY-STOKES-BRINKMAN EQUATIONS.SIAM JOURNAL ON SCIENTIFIC COMPUTING,32(2),855-874.
MLA	Xu, Xuejun,et al."A NEW DIVERGENCE-FREE INTERPOLATION OPERATOR WITH APPLICATIONS TO THE DARCY-STOKES-BRINKMAN EQUATIONS".SIAM JOURNAL ON SCIENTIFIC COMPUTING 32.2(2010):855-874.