Acta mathematica scientia, Series B >
CONVERGENCE OF THE CRANK-NICOLSON/NEWTON SCHEME FOR NONLINEAR PARABOLIC PROBLEM
Received date: 2014-10-21
Revised date: 2015-03-11
Online 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).
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.
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 . DOI: 10.1016/S0252-9602(15)30083-7
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