Error control and adaptivity for a phase relaxation model

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	Error control and adaptivity for a phase relaxation model
	Chen, ZM ; Nochetto, RH ; Schmidt, A
	2000-07-01
发表期刊	ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE
ISSN	0764-583X
卷号	34 期号:4 页码:775-797
摘要	The phase relaxation model is a diffuse interface model with small parameter epsilon which consists of a parabolic PDE for temperature theta and an ODE with double obstacles for phase variable chi. To decouple the system a semi-explicit Euler method with variable step-size tau is used for time discretization, which requires the stability constraint tau less than or equal to epsilon. Conforming piecewise linear finite elements over highly graded simplicial meshes with parameter h are further employed for space discretization. A posteriori error estimates are derived for both unknowns theta and chi, which exhibit the correct asymptotic order in terms of epsilon, h and tau. This result circumvents the use of duality, which does not even apply in this context. Several numerical experiments illustrate the reliability of the estimators and document the excellent performance of the ensuing adaptive method.
关键词	phase relaxation diffuse interface subdifferential operator finite elements a posteriori estimates adaptivity
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000089499000003
出版者	E D P SCIENCES
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/15326
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.Univ Maryland, Dept Math, College Pk, MD 20742 USA 3.Univ Freiburg, Inst Angew Math, D-79104 Freiburg, Germany
推荐引用方式 GB/T 7714	Chen, ZM,Nochetto, RH,Schmidt, A. Error control and adaptivity for a phase relaxation model[J]. ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE,2000,34(4):775-797.
APA	Chen, ZM,Nochetto, RH,&Schmidt, A.(2000).Error control and adaptivity for a phase relaxation model.ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE,34(4),775-797.
MLA	Chen, ZM,et al."Error control and adaptivity for a phase relaxation model".ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE 34.4(2000):775-797.