Numerical methods for Stefan problems with prescribed convection and nonlinear flux

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	Numerical methods for Stefan problems with prescribed convection and nonlinear flux
	Chen, ZM ; Shih, T ; Yue, XY
	2000
发表期刊	IMA JOURNAL OF NUMERICAL ANALYSIS
ISSN	0272-4979
卷号	20 期号:1 页码:81-98
摘要	This paper deals with numerical methods for a class of nonlinear degenerate parabolic equations with nonlinear flux boundary conditions, which in particular includes the well-known continuous casting Stefan problem. A practical piecewise linear finite element scheme with numerical integration which is based on an implicit discretization of the diffusion and an explicit approximation of the enthalpy-dependent convection is proposed. The convergence of the scheme is proved without requiring the quasi-uniformity and the acuteness of the finite element meshes. The key ingredient of the analysis is an estimate on the fractional derivative in time of the discrete temperature which provides the necessary strong convergence property. The results of some numerical tests are provided in order to show the accuracy of the scheme.
关键词	piecewise linear finite elements numerical quadrature convergence Stefan problem with convection nonlinear flux
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000085067600004
出版者	OXFORD UNIV PRESS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/14991
专题	中国科学院数学与系统科学研究院
通讯作者	Chen, ZM
作者单位	1.Acad Sinica, Inst Math, Beijing 100080, Peoples R China 2.Hong Kong Polytech Univ, Dept Appl Math, Hong Kong, Hong Kong 3.Suzhou Univ, Dept Math, Suzhou 215006, Peoples R China
推荐引用方式 GB/T 7714	Chen, ZM,Shih, T,Yue, XY. Numerical methods for Stefan problems with prescribed convection and nonlinear flux[J]. IMA JOURNAL OF NUMERICAL ANALYSIS,2000,20(1):81-98.
APA	Chen, ZM,Shih, T,&Yue, XY.(2000).Numerical methods for Stefan problems with prescribed convection and nonlinear flux.IMA JOURNAL OF NUMERICAL ANALYSIS,20(1),81-98.
MLA	Chen, ZM,et al."Numerical methods for Stefan problems with prescribed convection and nonlinear flux".IMA JOURNAL OF NUMERICAL ANALYSIS 20.1(2000):81-98.