四阶/二阶椭圆界面问题的混合有限元方法  

Mixed finite element approach to fourth-order/second-order elliptic interface problems

作　　者：刘梦杰 贺明艳 LIU Mengjie;HE Mingyan(School of Sciences,Hangzhou Dianzi University,Hangzhou Zhejiang 310018,China)

机构地区：[1]杭州电子科技大学理学院,浙江杭州310018

出　　处：《杭州电子科技大学学报(自然科学版)》2025年第1期89-94,共6页Journal of Hangzhou Dianzi University:Natural Sciences

基　　金：国家自然科学基金项目(12171366)。

摘　　要：研究了一类带跳跃系数的椭圆界面问题,并将其转化为椭圆/混合椭圆界面问题。针对四阶/二阶椭圆界面问题,提出了一种混合有限元方法。对于四阶椭圆方程的非线性项,采用Picard迭代算法进行求解。通过一系列数值实验,得到了各变量在相应范数下的最优收敛阶。A class of elliptic interface problems with jump coefficients are studied and transformed into elliptic/mixed elliptic interface problems.In order to solve the fourth-order/second-order elliptic interface problem,a mixture method of mixed finite elements is proposed.For the nonlinear terms of the fourth-order elliptic equation,the Picard iterative algorithm is used to deal with it,and the optimal convergence order of each variable under its respective norms is obtained by calculation.

关 键 词：界面问题 Picard迭代 混合有限元 跳跃系数 最优收敛阶 

分 类 号：O241.82[理学—计算数学]