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Numerical approximation of the Cahn-Hilliard and Allen-Cahn equations with general nonlinear potential using the invariant energy quadratization approach
发布时间: 2018-09-11     14:45   【返回上一页】 发布人:张国栋


 北京师范大学数学科学学院

 

计算数学学术报告

 

 

报告题目:Numerical approximation of the Cahn-Hilliard and Allen-Cahn equations with general nonlinear potential using the invariant energy quadratization approach

 

报告人:张国栋烟台大学 )

 

时间地点:9月17日下午13:30 教八401

 

邀请人: 张辉

 

摘要In this paper, we carry out stability and error analyses for two first-order, semi-discrete time stepping schemes, which are based on the newly developed Invariant Energy Quadratization approach, for solving the well-known Cahn-Hilliard and Allen-Cahn equations with general nonlinear bulk potentials. Some reasonable sufficient conditions about boundedness and continuity of the nonlinear functional are given in order to obtain optimal error estimates. The well-posedness, unconditional energy stabilities and optimal error estimates of the numerical schemes are proved rigorously. Through the comparisons with some other prevalent schemes for several benchmark numerical examples, we demonstrate the stability and the accuracy of the schemes numerically.