一维椭圆型方程界面问题的弱有限元方法  

Weak Finite Element Method for Interface Problems of One Dimensional Elliptic Equations

作　　者：何朝葵[1] 朱永忠[1] 杨凤莲 HE Zhao-kui;ZHU Yong-zhong;YANG Feng-lian(College of Science,Hohai University,Nanjing 211100,China)

机构地区：[1]河海大学理学院,江苏南京211100

出　　处：《数学的实践与认识》2023年第8期237-247,共11页Mathematics in Practice and Theory

基　　金：高等学校大学数学教学研究与发展中心2022年教学改革项目(CMC20220203);中国高等教育学会2022年度高等教育科学研究规划课题高等理科教育改革实践研究重点课题(22LK0303);江苏省高校“大学生劳动教育”“基础课程群”专项重点课题(2021JDKT017);江苏省高等教育教改研究立项课题重点项目(2021JSJG090)。

摘　　要：界面问题是一个比较受关注的课题,对于一维的椭圆型方程,如果系数不连续或源项是奇异的,在解区间内则会产生界面.弱有限元方法是一种比较新的数值计算方法,在多个领域的应用表明:与经典有限元方法比较,弱有限元方法具有计算格式稳定和数值解精度高的优势.为此,研究弱有限元方法在一维界面椭圆型方程的应用是有意义的,通过引入一个参数,把含界面椭圆型方程问题变成两个混合边值问题来处理,推导出相应的弱有限元方法计算格式,并通过数值算例对计算格式进行验证,数值结果证明了计算格式的有效性和可行性.The interface problem is a subject of more concern.For one-dimensional elliptic equations,if the coefficients are discontinuous or the source term is singular,the interface will be generated in the solution interval.The weak finite element method is a relatively new numerical calculation method.Its application in many fields shows that compared with the general finite element method,the weak finite element method has the advantages of stable calculation format and high accuracy of numerical solution.Therefore,it is meaningful to study the application of weak finite element method in one-dimensional interface elliptic equation.By introducing a parameter,the elliptic equation with interface is transformed into two mixed boundary value problems,and the corresponding weak finite element method calculation format is derived.Numerical examples are used to verify the calculation format.The numerical results prove the validity and feasibility of the calculation format.

关 键 词：界面 有限元方法 弱有限元方法 变系数 奇异源项 

分 类 号：O241.82[理学—计算数学]