求解带有Robin型跳跃条件一维界面问题的浸入有限元方法  

AN IMMERSED FINITE ELEMENT METHOD FOR SOLVING 1D INTERFACE PROBLEMS WITH ROBIN TYPE JUMPS

作　　者：秦芳芳 张金金 纪海峰[1] 陈艳萍 Qin Fangfang;Zhang Jinjin;Ji Haifeng;Chen Yanping(School of Science,Nanjing University of Posts and Telecommunications,Nanjing 210023,China)

机构地区：[1]南京邮电大学理学院,南京210023

出　　处：《计算数学》2024年第4期516-528,共13页Mathematica Numerica Sinica

基　　金：国家自然科学基金(12371370、11801281);国家自然科学基金重点项目(11931003);南京邮电大学引进人才科研启动基金(NY223127);江苏省博士后科研资助项目(2020Z380)资助.

摘　　要：浸入有限元方法是一类基于非拟合网格求解界面问题的有效数值方法.目前,对带有传统界面跳跃条件的界面问题,浸入有限元方法已有许多研究,而对带有Robin型跳跃条件的界面问题,该方法的研究较少.本文针对带有Robin型跳跃条件的一维界面问题提出了浸入有限元方法.本文证明并通过数值算例验证了浸入有限元空间的最优逼近性以及浸入有限元方法的最优收敛性.Immersed finite element methods are a group of effective numerical methods for solving interface problems using unfitted meshes.Currently,there are many works on immersed finite element methods for solving interface problems with traditional interface jump conditions.However,there is limited research on interface problems with Robin type jump conditions.In this paper,an immersed finite element method is proposed for solving one-dimensional interface problems with Robin-type jump conditions.The optimal approximation properties and the optimal convergence of the proposed immersed finite element method are proved rigorously.Some numerical examples are provided to validate the theoretical results.

关 键 词：界面问题 Robin型跳跃条件 浸入有限元 非拟合网格 

分 类 号：O241.82[理学—计算数学]