求解变系数Cahn-Hilliard-Brinkman方程有限元方法的误差分析  

Error Analysis of Finite Element Method for Solving Cahn-Hilliard-Brinkman Equation with Variable Coefficients

作　　者：张若琦 贾宏恩 ZHANG Ruoqi;JIA Hongen(College of Mathematics,Taiyuan University of Technology,Jinzhong 030600,China)

机构地区：[1]太原理工大学数学学院,山西晋中030600

出　　处：《应用数学》2020年第2期496-506,共11页Mathematica Applicata

基　　金：国家自然科学基金(11872264);山西省高等学校科技创新项目(2017119)。

摘　　要：本文研究求解变系数Cahn-Hilliard-Brinkman方程有限元方法的误差分析.在时间格式上采用能量凸分裂法以及在空间格式上采用混合有限元法进行离散,证明了全离散格式是能量衰减的.在误差分析中,利用Cauchy中值定理将含浓度和Peclet数的项分解为两项,结果表明所提出的格式在时间上是二阶精度的.In this paper,the error analysis of finite element method for solving cahn-hilliardbrinkman equation with variable coefficients is studied.The energy convex splitting method is used in the time scheme,and the mixed finite element method is used in the space scheme to discretize.It is proved that the full discrete scheme is energy attenuated.In error analysis,the term containing concentration and peclet number is decomposed into two terms by using cauchy mean value theorem.The results show that the proposed scheme is second-order accuracy in time.

关 键 词：Cahn-Hilliard-Brinkman方程 变系数 混合有限元法 凸分裂法 

分 类 号：O242.21[理学—计算数学]