CONVERGENCE OF THE CRANK-NICOLSON/NEWTON SCHEME FOR NONLINEAR PARABOLIC PROBLEM

doi:10.1016/S0252-9602(15)30083-7

数学物理学报(英文版) ›› 2016, Vol. 36 ›› Issue (1): 124-138.doi: 10.1016/S0252-9602(15)30083-7

CONVERGENCE OF THE CRANK-NICOLSON/NEWTON SCHEME FOR NONLINEAR PARABOLIC PROBLEM

冯新龙¹, 何银年²

1. College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, China;
2. Center for Computational Geosciences;School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an 710049, China

收稿日期:2014-10-21 修回日期:2015-03-11 出版日期:2016-01-30 发布日期:2016-01-30
作者简介:Xinlong FENG,E-mail:fxlmath@xju.edu.cn;Yinnian HE,E-mail:heyn@mail.xjtu.edu.cn
基金资助:
This work is in part supported by the Distinguished Young Scholars Fund of Xinjiang Province(2013711010), NCET-13-0988 and the NSF of China(11271313, 11271298, 61163027, and 11362021).

CONVERGENCE OF THE CRANK-NICOLSON/NEWTON SCHEME FOR NONLINEAR PARABOLIC PROBLEM

Xinlong FENG¹, Yinnian HE²

1. College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, China;
2. Center for Computational Geosciences;School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an 710049, China

Received:2014-10-21 Revised:2015-03-11 Online:2016-01-30 Published:2016-01-30
Supported by:
This work is in part supported by the Distinguished Young Scholars Fund of Xinjiang Province(2013711010), NCET-13-0988 and the NSF of China(11271313, 11271298, 61163027, and 11362021).

摘要/Abstract

摘要：

In this paper, the Crank-Nicolson/Newton scheme for solving numerically second-order nonlinear parabolic problem is proposed. The standard Galerkin finite element method based on P₂ conforming elements is used to the spatial discretization of the problem and the Crank-Nicolson/Newton scheme is applied to the time discretization of the resulted finite element equations. Moreover, assuming the appropriate regularity of the exact solution and the finite element solution, we obtain optimal error estimates of the fully discrete Crank-Nicolson/Newton scheme of nonlinear parabolic problem. Finally, numerical experiments are presented to show the efficient performance of the proposed scheme.

关键词: nonlinear parabolic problem, Crank-Nicolson scheme, Newton method, finite element method, optimal error estimate

Abstract:

Key words: nonlinear parabolic problem, Crank-Nicolson scheme, Newton method, finite element method, optimal error estimate

中图分类号:

65N30

冯新龙, 何银年. CONVERGENCE OF THE CRANK-NICOLSON/NEWTON SCHEME FOR NONLINEAR PARABOLIC PROBLEM[J]. 数学物理学报(英文版), 2016, 36(1): 124-138.

Xinlong FENG, Yinnian HE. CONVERGENCE OF THE CRANK-NICOLSON/NEWTON SCHEME FOR NONLINEAR PARABOLIC PROBLEM[J]. Acta mathematica scientia,Series B, 2016, 36(1): 124-138.

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CONVERGENCE OF THE CRANK-NICOLSON/NEWTON SCHEME FOR NONLINEAR PARABOLIC PROBLEM

CONVERGENCE OF THE CRANK-NICOLSON/NEWTON SCHEME FOR NONLINEAR PARABOLIC PROBLEM

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