THE SPACE-TIME FINITE ELEMENT METHOD FOR PARABOLIC PROBLEMS

Applied Mathematics and Mechanics (English Edition) ›› 2001, Vol. 22 ›› Issue (6): 687-700.

THE SPACE-TIME FINITE ELEMENT METHOD FOR PARABOLIC PROBLEMS

李宏, 刘儒勋

Department of Mathematics, University of Science and Technology of China, Hefei 230026, P.R.China

收稿日期:1999-12-14 修回日期:2000-11-28 出版日期:2001-06-18 发布日期:2001-06-18
通讯作者: LIU Ci-qun,LIN Zong-chi
基金资助:
the National Natural Science Foundation of China (19771083);the National Science Foundation of American (INT 9601084)

THE SPACE-TIME FINITE ELEMENT METHOD FOR PARABOLIC PROBLEMS

LI Hong, LIU Ru-xun

Department of Mathematics, University of Science and Technology of China, Hefei 230026, P.R.China

Received:1999-12-14 Revised:2000-11-28 Online:2001-06-18 Published:2001-06-18
Supported by:
the National Natural Science Foundation of China (19771083);the National Science Foundation of American (INT 9601084)

摘要/Abstract

摘要： Adaptive space-time finite element method, continuous in space but discontinuous in time for semi-linear parabolic problems is discussed. The approach is based on a combination of finite element and finite difference techniques. The existence and uniqueness of the weak solution are proved without any assumptions on choice of the space-time meshes. Basic error estimates in L^∞(L²) norm, that is maximum-norm in time, L²-norm in space are obtained. The numerical results are given in the last part and the analysis between theoretic and experimental results are obtained.

Abstract: Adaptive space-time finite element method, continuous in space but discontinuous in time for semi-linear parabolic problems is discussed. The approach is based on a combination of finite element and finite difference techniques. The existence and uniqueness of the weak solution are proved without any assumptions on choice of the space-time meshes. Basic error estimates in L^∞(L²) norm, that is maximum-norm in time, L²-norm in space are obtained. The numerical results are given in the last part and the analysis between theoretic and experimental results are obtained.

中图分类号:

O242.21

李宏;刘儒勋. THE SPACE-TIME FINITE ELEMENT METHOD FOR PARABOLIC PROBLEMS[J]. Applied Mathematics and Mechanics (English Edition), 2001, 22(6): 687-700.

LI Hong;LIU Ru-xun . THE SPACE-TIME FINITE ELEMENT METHOD FOR PARABOLIC PROBLEMS[J]. Applied Mathematics and Mechanics (English Edition), 2001, 22(6): 687-700.

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THE SPACE-TIME FINITE ELEMENT METHOD FOR PARABOLIC PROBLEMS

THE SPACE-TIME FINITE ELEMENT METHOD FOR PARABOLIC PROBLEMS

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