双曲型界面问题的变网格低阶有限元方法  

Low Order Finite Element Method with Moving Grids for Hyperbolic Interface Problems

作　　者：关宏波 洪亚鹏 曲双红 GUAN Hongbo;HONG Yapeng;QU Shuanghong(College of Mathematics and Information Science,Zhengzhou University of Light Industry,Zhengzhou 450002,China)

机构地区：[1]郑州轻工业大学数学与信息科学学院

出　　处：《应用数学》2020年第1期146-153,共8页Mathematica Applicata

基　　金：国家自然科学基金(11501527);郑州轻工业大学青年骨干教师基金(2016XGGJS008)、博士基金(2015BSJJ070)、研究生科技创新基金(2018018)

摘　　要：本文针对双曲型界面问题,讨论线性三角形有限元的变网格方法,其主要思想是针对空间变量采用有限元离散,对时间变量采用差分离散,但不同时刻的有限元剖分网格可以不同.在不引入Ritz投影这一传统分析工具的情况下,得到了相应的最优误差估计结果.最后将该方法进行推广应用,为界面问题的数值计算提供另一种解决途径.This paper discusses a linear triangular finite element method with moving grids for the hyperbolic interface problems.The general idea is applying finite element method in space and choosing difference method with respect to the time variable,respectively,but the grids can be different when the time varies.Some optimal order error estimates are obtained without introducing the Ritz projection,which is thought to be a conventional analysis tool.Lastly,the method is extended to the applications in some other cases.The result could provide another option of numerical method for interface problems.

关 键 词：双曲型界面问题 线性有限元 全离散 变网格 最优阶误差估计 

分 类 号：O212.21[理学—概率论与数理统计]