李娟. 对流Cahn-Hilliard方程的高精度有限差分方法[J]. 云南大学学报(自然科学版), 2017, 39(4): 513-522. doi: 10.7540/j.ynu.20160486
引用本文: 李娟. 对流Cahn-Hilliard方程的高精度有限差分方法[J]. 云南大学学报(自然科学版), 2017, 39(4): 513-522. doi: 10.7540/j.ynu.20160486
LI Juan. High accurate difference method for the convective Cahn-Hilliard equation[J]. Journal of Yunnan University: Natural Sciences Edition, 2017, 39(4): 513-522. DOI: 10.7540/j.ynu.20160486
Citation: LI Juan. High accurate difference method for the convective Cahn-Hilliard equation[J]. Journal of Yunnan University: Natural Sciences Edition, 2017, 39(4): 513-522. DOI: 10.7540/j.ynu.20160486

对流Cahn-Hilliard方程的高精度有限差分方法

High accurate difference method for the convective Cahn-Hilliard equation

  • 摘要: 研究对流Cahn-Hilliard方程的高精度有限差分方法.给出三层线性化紧差分格式及其解的存在唯一性,利用能量分析方法证明数值解在L∞范数下时间方向二阶、空间方向四阶收敛.最后通过数值算例,验证差分格式是有效的.

     

    Abstract: It is devoted to the study of high accurate method for the convective Cahn-Hilliard equation.A three level linearized compact difference scheme is derived,and the unique solvability is given.The unconditional convergence of the difference solution is proved by energy method.The convergence order is two in time and four in space in the maximum norm.Some numerical examples are presented to demonstrate the theoretical results.

     

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